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-  ,ti25\ai^ 


An  Investigation  into  the  Elastic  Constants 

ot"  Rocks,  More  Especially  with  Reference 

to  Cubic  Compressibility 


HY 


TRANK  I)   ADAMS  ani.  ERNEST  G.  COKER 


\VASHIN(.T<)N,   D,  L 

PuHishctl  liv  the  Cairugie  In^litution  ut  Wj^hmijtjii 

jui.c.  tyuo. 


An  Investij^ation  into  the  Elastic  Constants 

of  Rocks,  More  Especially  with  Reference 

to  Cubic  Compressibility 


BY 


KRANK  I).  ADAMS  ani.  hRNfcST  G.  COKER 


'Z7 


WASHINCTON,   I).  C. . 

I'ublishcil  !•>  the  (  arncgie  Inslitutiun  of  Washington 

June,  1000. 


CARMlA,"    INSrUUTKJN  Ol-  WASHINGTON 

I'llll  ICATillN    N.p.     fO 


I'KKSS    OF    CIRSON    BROS. 
WASHINGTON,  D.   C. 


i 


CONTKNTS. 


lan  one  Miiitrul: 


Iiitrcjdiictjiiri 

Metl„„l,  «l„d,  may  I*  um-.I  in  ilu-  IK-H„,u,uii.m  .,(  i:i.,.,ii.- i„„s,  „„, 

A,.,.luMl...n  ,  f  the  M,, f  sin.pU-  Cn„„.,cvsi.,n  ,„  ,1,..  lH-,>r,„i„.,„„„ 

f)rcssilii|ity  i.f  Mil. lis 
Applicati..!!  „f  .Ik-  .\k-.l,.Hl  „f  Simple  0.n,pa>.i„i.  i„  ilu-  IVlvrt, 

pri-ssiliiliiv  of  Kinks 
The  MetlHid  ,,f  Measiirenunt 

The  iilastie  Omstant.  „f  k,„ks  C..mp..se.l  „f  ,,  Siir.-K^  Mi.ierul- 
Maililes  and  I.iniest.iiie>  ~ 

I.    Dlack  IteUian  MarMe  i"  N.iir  l-iti'i 

3.  Whit.-  Carrara  Mirlilt 
.1.    While  \eriiii.nt  Marlile  

4.  Ttnnesvte  .Marble  (■•  I'ink  i'enneswe  ") 

•r.      ...      .  ^'   '''"'■-''''''■'""•'■'■""'""  'ini'-'^l'ne,  M.mlreal.  Canada 
The  hlastic  C.mstants  m   K„eks  C..ni|K.Hvl  „f  in„re  th 
Acid  Plnlimic  Rucks  — 
C.ranile 

6.  Cranile  — Havenii,  Italy 

7.  C.ranite— Peterhead,  Si'iilland 

«.  Granite     I.ily  r.ake,  .Neiv  Hrinisvvick,  Canada     . 
9    Granile-Westerlv.  Uh.ide  Isl.in.l,  T   S.  .\ 

10.  Granite -Onincy,  Mas.i.ichiisetts,  ('.  S    .\ 

11.  Granite     Stansle.i.l.  I'r.ivinii  ,,f  (Jiiel,ec.  C.ina.la 
.\epheline  Svenite: 

i.v    N'eplii'hne  Svenile,  Mmiireil,  Can.i':.i 
li.l^ie  I'liitcnic  U.K-ks 

t.\.   Aii„rth..siie,  New  Glas-.nv,  IVninee  ,,f  (  Hu'Ikt   C.ini.l. 
14.    Fvsse.xile,  .\I...mt  .Johnson,  Province  of  oaelH-c,  Canada 
IS    Green  G.dihn.,  New  Glasgow,  Province  of  '  )„elK'C,  Canada 

K     '"'^""■'  »'■'•«•*.  S»'lln.rv,  Province  of  M,„.,rio,  Canada 
Seduneniary  Nocks  (Cl.istic)     • 

17.  Sandstone,  Clevel.ind.  '  i|,io 

The  Elastic    Constants  of  Glass 

Summary  of  Kesnits 


■I'  "laerials 
•  f  the  Com- 


iii.ilioii  ,if  the  Coni- 


I.S 
JO 


it) 
38 

JI 


40 

4-' 

i  i 


SJ 
.5  5 
57 

60 

60 


'L'51-6 


liip 


LIST  OF  PLATE^- 


Plate      I. 

II 

III 

IV. 

V. 

VI. 

VII. 

VIII. 

IX. 

X 

XI 

XII. 

XIII. 

XIV. 

XV. 

XVi 


Hl,uk  H( l«ian  Marble   '^ 

C;irr.ira  Marble     ,,, 

\irninni  Marlile                           ^„ 

Marble-  Tinness«i-       I'iiik  rinnes^it" ) ,„ 

Treiilim  Liiiiesiim        Momrial,  Canada \j 

Oranile — Huvrnii,  Italy   

OraiiilP     I.ily  l.akt.  Canaila    .             ',j( 

OraTiili-     Weslerlv.  Rliuile  Uland ,„ 

C.ranilf     Quim-y,  Massailni  iits ,, 

Ctranilc     St:instra<l,  Caiia.la              ,f, 

Neplulim-  Syenite     Mi.ntreal,  Canada ,fj 

Aniirthosite  —New  C.l.is^rim.  Cana(la    ,„ 

Essexite -  '...nuit  Ji.linsm,  Canada     ,^ 

Green  Galibni  -Ne'v  ClasKinv,  Cana<la ,,, 

Olivine  I)iaUis«-     ;     "uiry,  C.in.ida .    .  .    ',), 

S;in(lsti>ne    Cleve           ( ihiu      ^ 

3 


AN  INVKSTIGATION  INTO  THH  Hl.ASTIC  CONSTANTS  OF  ROCKS, 

MORli  HSriXlALLY  WITH  RHl-T'RHNCi;  TO  CUBIC 

COMl'KHSSllMLlTY. 


INTRODUCTION. 

The  question  as  to  the  amount  of  cubic  compression  which  rocks  may 
undergo    under    the  stresses   to   which   they   are  subjected   in   the  earth's 
crust  is  one  which  lias  a  direct  bearing  on   inanv  very  important    problems 
in  geophysics.      It  is.  liowever,  a  subject  whieli  has  been   l)Ul   httle  in\isii 
gate<l  as  the  experimental  dilVicnlties  connected  with  it  are  vervconsidi  ralile 
The  importance  of  a  series  of  determinations  of   the  cubic  compressibilil\ 
of  a  few   tyjiical    pUitonic  i.,'ueous  rocks  was   some    time  since  impressed 
upon  tlie  authors  bv  Mr  G    IC   Gilbert,  with  a  request  that  if  possible  they 
should  make  such  determinations  in  connection  ivilh  the  researches  on  rock 
deformation  which  are  now  being  carried  oiu    at    McGill    University  imder 
the  auspices  of  the  Carnegie  Institution  of  Washington      An  examination 
of  all  the  direct  methods  proposed  or  adopted  l"or  the  measurement  of  the  cubic 
cimipressibilitv  of  solids  showed  that   none  of  these  could  be   satisfa<toril\ 
applied  to  such  materials  asrocks.but  the  indirect  iiuthorls  based  on  Hook's 
law  and  which  have  been  applied  to  metals  and  other  couqiaci  isotropic  bndirs 
having  an  approximately  perfect  elasticitv  promisid  to  give  satisfaclor'   re 
suits  if  applied  to  certain  rocks,  more  ispeciall\  to  the  class  of  roeks  referred 
to  above,  viz,  the  acid  and  basic   plutonie   rocks,  which  form   the   great ir 
part  at  least  of  the  outer  portions  of    the  earth's  crust       Tlu'  present  i)aper 
sets  forth  the  methods  adopted  and  the  results  obtained 

The  work  which  was  carried  out  in  the  laboratories  of  .MeGil!  fniversitx  was 
connneneed  bv  the  authors  whose  names  apiH'ar  on  the  title  page,  and  was 
carried  well  towards  cnm|)letiou  when  I)r  Coker  w.e^  called  to  lake  the 
professorship  of  mechanical  engineering  iti  tlie  I'iusburv  Technical  Inslilule 
of  London,  Ivngland  He  was  accordinglv  obliged  to  give  iq)  the  work  nf 
the  research  and  his  place  was  taken  bv  Mr  Charles  McKergnw.  lecturer 
in  mechanical  engineering  in  .McGill  University,  but  who  imniedi.itely  on 
the  completion  of  the  work  was  appointed  to  the  professorship  in  mechanical 
engineering  in  the  University  of  Virginia  .Marge  mnnberof  the  very  care 
ful  measurements  of  elastic  ccmstants  which  are  given  in  tlie  paper  were 
made  by  the  latter  gentleman 


AN    INVIiSTlGATION    INTO    TllIJ 


METHODS  WHICH  MAY    BE    USED  IN    THE    DETERMINATION  OF  THE 
ELASTIC  CONSTANTS  OK  MATERIALS. 

Till-  (IcUTiiiiiiatioii  of  tlu'  cubic  c()niprissil)ility  of  solid  Mibstanccs  is,  as 
above  inciilioiud.  beset  with  serious  (lilViculties  On  the  one  hand,  every 
direct  uielhod  whicli  has  been  siit;L;esle(!  ])rescnts  experiiuental  (HiViculties 
which  li'ud  to  impair  its  accuracy,  whiU'  on  tlie  other  hand  tlie  indirect 
methods  are  based  on  assumptioiisas  to  the  isotropy  of  tlie  materials,  which 
are  not  \varrante<l  in  the  case  of  certain  rocks  TIh'  indirect  methods  tlc- 
penilini;  on  the  theorv  of  elastieit\-  are  capable  of  considerable  variation,  ai:d 
it  is  of  interest  to  txamine  them  in  some  detail  in  order  to  see  whether  certain 
of  tluni  at  least  may  not  be  di'peiided  r.jjon  to  uive  reliable  and  satisfactory 
results 

The  determination  of  the  elastic  constants  of  metals  has  cnRafjcd  the 
attentionof  m mv  physicist'^  ai'.d  at  ihe  present  time  a  larj^e  amount  of  infor- 
mation exists  as  to  the  values  of  these  constants  for  various  metals. 

It  is  well  known  that  in  homo;;eneons  clastic  substances  a  sir-')le  compres- 
sion stress  causes  .1  lateral  strain,  which  bears  a  lixed  ratio  to  the  compression 
strain  for  anv  p.irticul.ir  subslauce  within  tl.e  limit  of  elasticitx'.  If.  then,* 
we  call  p,  the  stress  on  a  ])lane  perpendicular  to  v  in  the  direction  .v,  and  e^ 
the  corresponding;  strain,  then  for  a  'inct  compression  stress  />,  there  will 
be  a  str.iinin  the  direction  of  this  stre^-,  i  amount  />,  /•,',  where  /•,'  is  Vonnj^'s 
modulus,  and  lateral  strain  of  mai;ullu(le  p,  nili.  where  m  is  the  ratioof  the 
lontjitudiual  ciiiupression  to  the  lalerd  ixtension  per  tmit  of  length 

If  we  suppose  f\irther  that  a  bod \  is  subjected  to  cubical  stress  of  in- 
teusilv  /!,,  we  easily  see  that  for  small  and  therefore  superposable  strains  the 
cubical  strain  i ,  is 


\ 


r  =  ?<p, 


ml: 


and  since  llu'  modulus  of  cubical  compressibility  /^  is  the  ratioof  the  stress 
per  imit  of  area  to  the  cubical  strain  produced,  we  have 


D  = 


t'r. 


E. 


T.  Ill  -  2 

Hence  if  wc  know  /■.'  and  m  we  can  calculate  the  value  of 
Further,  it  is  shown  in  treatises  on  elasticity  that  if  C  is 
shear,  then 


modulus  of 


2    III   i    I 


E 


*Sce  Ewin^j's  Streiijilli  nf  Materi.ils,  Ch.ijiter-^  I  \-  II, 


ELASTIC    CONSTANTS    OF    ROCKS. 


i 


and  since  C  and  E  arc  quantities  which  can  be  ascertained  by  experiment,  we 
can  from  them  calculate  »i  and  l> 

In  an  important  paper  by  Nagaoka*  this  latter  method  has  been  used  to 
determine  the  elastic  constants  of  a  series  of  rocks  The  value  of /•'was  deter- 
mined bvsupixirlini;  a  bar  at  the  ends  and  measurins  the  angular  change  at 
the  sup])ort  due  to  a  j;iveu  load  applied  at  the  center;  the  value  of  /•,'  is  then 
obtained  bv  ll'.e  formula  /■.  -  .;a7'  4/11/  H.  wlure  /  is  the  length  of  the  bar 
between  the  s\ip|)orts,  />  is  the  breadth  of  the  bar.  1!  the  depth,  and  II  the 
anj;ular  chani;e  at  the  euils  for  a  load,  11'  In  order  to  determine  the  value 
of  m,  a  s|Hcimeii  of  rectausular  section  was  twisted  by  a  given  tortpie,  T, 
and  the  amount  of  the  strain  measured  It  has  been  shown  by  St  V'enant 
that  for  such  a  case  the  value  of  ("  is  given  b\  the  I'ormiila 

■'    tan  h  [2)1  +  1 1 


r  =.  ciih" 


"■] 


l\ 


wlure  /'  is  the  angular  change,  and  from  this  formula  values  <  if  C"  were  calculated 
from  the  observations 

This  meth<id  appears  to  us  to  be  open  to  some  minor  objecti<ins  in 
that  the  formula  for  determiiiiiig  /:  is  based  upon  a  theory  of  llexure,  which 
altlKuigh  sullieient  for  mauv  |5urpo>;es  is  nevertheless  I'ulv  approximate,  and 
it  is  well  known  that  values  of  /•,"  obtained  by  llexure  exixriments  in  this 
manner  often  differ  from  the  values  of  /■.  obtained  bv  direct  compression 
experiments  by  not  inconsiderable  amoimts 

F;:rther.  in  exi)erimeuts  upiin  the  (klliclion  of  beams  cut  from  rock",  it  is 
dilVieult  to  obtain  eonsistenl  readings,  because  of  the  timeelTeel  of  tlie  load- 
ing, and  this  dilVieuIty  is  noticed  in  the  jiaper  cited 

As  an  example  of  the  results  obtained  in  this  way.  we  niav  (ptotc  the 
results  of  certain  experiments  made  bv  us  with  a  pure  white  marble  from 
Vermont. 

Lath-shaped  pieces  of  the  marble  were  carefully  prepared  and  were  sus- 
pended on  two  wedge  shajjcd  supports  and  then  loaded  in  the  middle  The 
weights  were  placed  in  a  light  brass  pan.  hanging  from  a  thick  wire  which 
passed  over  the  middle  of  the  lath  and  lav  llat  upon  it. 

Each  experiment  occupied  about  half  an  hour,  and  the  deflection  was 
measured  by  attaching  a  scale  to  the  1  larbic  and  reading  it  with  reference 
to  a  thin  wire  stretched  in  front  of  the  specimen,  a  properly  moimted  tele- 
scope being  employed  for  this  purpose  The  marble  was  in  all  cases  placed 
so  that  its  broader  surface  rested  on  the  terminal  supports. 


♦lilastic  Ciinstants  of  Kocks  and  the  Veloeity  of  Seismic  \V:!vts.    H.   Nagaoka. 
Mag.,  Vol.  L,  i<)<x),  p.  5j. 


Phil. 


8  AK   IwnsTlOTlON   INTO  THE 

Of  the  several  experiments  inai.e  two  may  I)e  selected.     The  pan  and  wire 
in  each  case  \vei;;1n'(l  ,,  imnees 

In  the  first  experiment  the  marhle  h:i(l  the  fdUowinR  dimensions:     I,eni.'th, 

ij  inelies;  length  l)et  ween  snpjxirts,  ii  inelii.;  breadth,  i2,si)  inches:  thick 

ness,  o  284  to  0  2<)S  inch. 

The  figures  obtained  are  as  follows: 

lach. 

Lorwl  with  jun  only  (takcnas  zero  poin!) 0.486 

wiih  pan  plus  4  imtuTs 4''7 

s  .miK-cs ■•*** 

4S<) 

I .'  "Hijiei's  ^ 

Id  imiiccs  ■ 4y" 

rn.mi.cs  491 

J  \  oniKcs  -4''* 

JS  MUIK'CS  '4'*' 

;j  utiiu't'S  ■  ■  -4'*^ 

V»  imtift's  -VfA 

40  ruiucos  4*'/ 

44  niim-i's  -4*)" 

IS,,1M1'1-S  ■■'-"" 

5-..i..MT^  •>"' 

5'j  tnuicc-.;  .."»'\^ 

r.ooiinfrs  ■^"'^ 

(.11  oiim-is  (:il'lu  J  niiiiuu-.!  ^^^' 

(1)  iriiiu-c>-..  -^'^ 

(il  iiniici";  iMliir  il  iiiiium  1                                                               .^''' 

(<<•  nlliu-o-i  ■^'' 

(,■^  ..lino-  ••''■■'* 

1.^  iiiim-i...  (alu  1    1 5  liiiiiut^-^i  ■■'-" 

70  '.itn.;i-  ■"'-* 

-2  ..iiiut"-  "*" 

;_' .imKi- latlir  1  )iumiu  1  ■.^-- 

7  }  (iiinccs  ..^  -  • 

7..  ..inu-.-.;  ■-'^-'■'" 

■i>  ..iHH'i"-  I  HUT  I  |.  iiiimitc-.l  .  ■^'-' 

7'-   "Hint—.  ..^.V^ 

^....mu•.-  .  ■^'4 

,^.  I  ..iin.T    I J  I'll  r  J  iiiiinm-.  ni'.viii'^'  I.!--!  St" 

v:  ..iin.a-  .^41 

,^.'  ..inui- l.iltir  1  ;.  iiiimili-.  '  -^4.1 

--'  .ilinc'cs  i\ui.;lit  rc.liux'il,  l.ir.'C  pcrm.inciu -i  1 1  -S^^  ■ 

S4  iniiiccs  ■■^4/ 

-■(1  iiiiiu-fs  ■S4'l 

M.  .mncis  iLiltir  i   iiiiiniu-;  l.i..kui  ,S.S4 

T.>!  il  fknrrti..n  I     f.irc  lirnkinc; "''4 


'f 


KLASTIC  CONSTANTS  OF  ROCKS. 


In  the  second  cxpcim  Jilt  the  marble  lathwa;  longer  and  at  the  same  time 
somewhat  thicker.  Its  dimensions  were  as  follows:  Length,  16  inches;  length 
between  supi)cirts,  .'.s  iiulies;  breadth,  i  23<)to  i  ^84  inches;  thickness,  347  to 
.,^56  inch. 

Inch. 

I.uacl  with  pan  only 343 

with  pan  plus  s  uum-cs.  .  349 

16  onnct'S .i^S 

J4  ounces 3*9 

24  ounces  (after  i  J  niiuules) 39' 

25  ounces 4^1 

32  ounces 4**' 

32  ounces    (alter  1 J  niimues) 4^3 

36  ounces 43^ 

40  ounces    4*^ 

I.nirl  witli  i)an  unly  (\vei;4ln  rem.. veil,  lari."-  pewi'  .iiciit  set) 412 

with  pan  plus  40  ounces  (after  2  nr'.uites) 47< 

44    ounces 492 

44  tiunces  {afle.  a  fc.v  ..^ee.ilKis) ..SOO 

4  (  ounces  (after  i  niimite;  limke)      520 

Total  <leilecf.,.i '77 

Here  it  will  be  noticed  thai  wlu  11  a  ccrlaiu  load  is  reacherl  a  .listinct  move- 
ment sets  in  and  is  maintained  without  anv  further  increase  of  load,  the 
in.)vement  ^'Dwiii'^  in  aiirxiiit  as  the  limit  of  the  strenj;lh  of  the  rock  is 
appr.)  tolled  and  pr.)dMcin'4  a  permanent  set. 

Hxpei.ments  on  the  (Uteniiination  of  the  elastic  constants  of  rocks  when 
snbjected  to  twist  were  also  fmind  to  lie  frequently  nns.itisfactor\-,  owing  to 
the  low  nlliniite  shearing  values  of  many  rocks 

While  a  glance  at  the  list  of  rocks  whose  elastic  const  -.nts  ha  ve  been  measured 
by  Xagaoka  will  at  one"  show  that  nio-.t  of  them  are  rocks  whose  elasticity 
must  he  of  a  verv  imperii ct  kind,  c  a  ,  weathere  1  clay  slate,  .-^chalstein,  tnfT. 
etc.;  the  method  which  he  has  employed  for  the  deterniinat'di!  of  Voting's 
modulus  gives  verv  low  results,  even  in  the  case  of  rocks  such  as  marble  and 
granite,  where  the  elasticity  might  be  supposed  to  be  of  a  high  order,  an.l 
comparalile  U)  that  .eliicli  these  rock?  have  been  sh.)wn  to  possess  in  the 
case  of  the  types  selected  for  investigation  in  the  present  paper  This  is 
shown  bv  the  following  figures  comprising  the  values  obtained  by  him  for 
each  of  the  marbles  and  granites  contained  in  his  list. 

t 

(VounK's 
Paleozoic  marble.  modulus). 

No.     1I.\ 10, 120,0fX) 

1  IB 7,0 so, 000 

I2.\ 5,440,000 

I3B 4.770,000 


Granite 

(Vour-s's 
modulus) 

N'lv 

r..)  (Slii.i             a)... 

6,i40,;kk) 

fiS  (Hit a           .         . 

,  .    2,Ss3,ooo 

71  (Hitachi) 

2,175,000 

,s6  (Hitachi; 

.  .    I,5SS,ooo 

52  (Hitachi)    

. .    3, 2')5,000 

lo 


A\    INVESTKIATION    INTO    THE 


Of  these  marbles  No  1 1 ,  if  a  meanof  the  two  readings  be  taken,  has  about  the 
same  moduUis  as  the  average  of  lliose  on  ouriist,  wl'^le  N'o.  12  is  very  mucli 
lower  Thehishest  value  tjiven  for  an v  f;ranitein  Xai;  ka'slist,  viz,  No  Cm),  is 
soMRwlialhi^lhertlian  that  of  the  lowest  of  the  granites  in  our  series,  that  from 
Stanstead  Tile  other  ijrauites  exaiuiiied  by  \aj;aoka  have  values  for  /•.' 
assii;ned  lo  lliein  which  are  so  low  that  tliey  are  eoiu;  arable  only  to  thai  of 
the  sandstone  in  oiu'  siri'S  Of  the  tliree  saiul'^'ones  ineluded  in  Naj;aoka  s 
list  the  Iznnii  sandstone  of  the  Mesozoie  has  niodidiis  of  1,322,000,  while 
til  other  two,  whieh  helonj;  to  tl'..'  Diluvium,  ha"  e  values  for  /  of  .s87,,S(K) 
au.i  sSs.iMKi.  respeetiNclv 

And  so  when  an  attempt  is  made  to  calculate  the  cubic  compression  l> 
from  the  values  vjiven  in  N'ai,'aoka's  list  and  obtained  by  his  method,  it  is 
found  that  a  nei;alive  valueis  actually  obtained  in  about  one  third  of  the  rocks 
which  he  has  examined  Mis  liijures,  however,  were  intended  chielly  for  the 
purpose  of  calculatim;  the  velocityof  the  propagation  of  earthquake  shocks 


mmm 


^  J  n  x^zm 


Vh\.  I.  —  IiistrnuuMit  fur  ili  icrniiniiiu'  tlic  iiumIiiIu^  <'1"  a  vimplo  striiiii. 

In  consequence  of  tlie  somewhat  unsatisfactory  results  obtained  in  our  pre- 
liminarv  experimeuis  with  this  method,  as  well  as  the  facts  with  regard  to 
N'aijaoka's  fiijures  just  mentioned,  it  was  decided  to  adopt  a  somewhat 
(lilTerent  method  and  one  wliich  avoided  both  torsion  and  flexure  and  depended 
sinqth  ou  str.iin  produced  bv  simple  comi)ressive  stress.  This  will  be  termed 
th<-   ■method  of  simple  compression 

.\moU;i  the  possil)le  indirect  methods,  this  seems  to  be  the  most  satisfae- 
tor\.  as  the  assuuiplious  necessary  in  the  calculation  ol  compressibility  are 
redui-ed  to  a  minimum,  and  the  ranifc  of  stress  for  which  the  ratio  of  stresr 
to  str.iin  is  practically  constant  is  <;reat  We  were  able  to  measure  the 
strains  obtained  very  accurately,  bv  means  of  an  ajjparatus  forminjjpart 
of  the  equipment  of  the  testini;  laboratory  of  Mi-Gill  University,  for  the 
use  of  which  we  are  indebted  to  Dean  Bovey. 

This  is  an  instrument  designed  by  Professor  Ivwing,  and  of  which  a  diagram- 
matic representation  is  given  in  figure  i,  in  which  A  is  a  specimen  of  the  rock 


ELASTIC   CONST.'*  VTS  OF   ROCKS 


II 


gripped  by  .,cre\vs  passir.),'  through  a  pair  of  collars,  fl,  which  are  i  2,s  inch 
apart,  to  which  latter  trctal  rods,  C,  are  attached.  The  upper  rod  carries  a  glass 
plate.  I),  with  a  fine  '.ine  scrat-hed  upon  it,  the  position  of  which  can  be 
adjusted  hv  a  screw.  /;,  while  t  le  lower  rod  carries  a  micrometer  microscope, 
F.  The  upiHT  and  lower  collars,  H.  are  connected  by  a  stud,  G,  the  upper 
on  •  engaging  with  tl  •  conical  hole  of  the  swivel  pi^ce //  in  the  lower,  and 
contact  is  maintained  by  a  spring,  /,  while  the  weights  of  the  microscope  and 
projecting  arms  are  balanced  by  lead  cylinders,  J  A  buzzer  was  attached  to 
the  upper  lead  cylinder  which,  when  operated,  caused  a  slight  vibration  in  the 
instrument,  producing  a  perfect  adjustment  as  the  pressure  was  applied. 


I'IG.  2. — I'ersl>cctive  view  of  lateral  extensomcter. 

The  proportions  of  this  instrument  were  so  adjusted  that  one  division  on 
the  micrometer  scale  corresponded  to  ,-'„„  of  an  inch,  and  before  using  it 
the  instrument  was  calibrated  li\  aid  of  a  Whitworth  measuring  machine 
and  was  found  to  be  in  correct  adjustment  This  instrument  enabled  us 
to  determine  the  modulus  of  simple  compressicm  with  great  accuracy. 

The  linear  strain  perpendicular  to  the  length  of  the  specimen  vas  measured 
bv  an  instrument  which  had  bet  ii  designed  by  EG.  Coker  some  time  previously 
for  experiments  on  the  lateral  strains  developed  in  metals  *    Figure  2  is 


♦."mjc  Proceedings  Royal  Soc.,  Uiiinburgh.     Session   1904-5.     Vol.  xxv,  pt.  VI. 


12 


AN    INVKSTIGATION    INTO    THE 


a  ili  ii;r;iintii:itic  view  of  tin-  appunitiis.  which  consists  iif  u  pair  of  lirass  lubes. 
li.  /(',  proviilcd  with  set  screws,  .1,  1',  for  atlachmiiit  to  tlic  spccinuii,  ami 
coiiiicctcil  to.i,'ctlicr  l)V  a  llcxiblc  steel  plate.  /',  lormiiiL;  the  fulcrum  The 
ends  of  the  tubes  near  the  fulcrum  plate  arc  pressed  apart  by  an  adjustable 
sprini;  S",  to  insure  a  uniform  pre-,snre  on  the  screw  points  -ripping  the 
specimen  On  the  opposite  eml  of  the  tubes  is  a  spriu','  finger,  /',  of  tb(]ny, 
pressing  aijainst  a  double  knife  cdi,'i-,  /v.se.ited  in  a  shallow  V  notch  cut  in  the 
end  of  the  other  arui  The  knife  ed;,'c  c.irries  an  adjustal)le  mirror,  M.  so 
til  at  if  anv  chalice  in  tlie  diameter  of  the  specimen  occurs  the  two  tubes 
move  relatively  to  one  another  in  a  horizontal  |)lane  and  tlureby  cause 
the  knife  edL;e  mirror  to  rotate;  the  rotation  of  this  latter  is  obbcrved  and 
measured  be  a  telescope  and  scale  placed  at  a  suitable  distance. 

I'or  convenience  in  adjustment  there  is  a  screw,  /.,  for  tiltins  the  apparatus 
.i1)oul  the  axis  of  the  ^'ripi)inL;  screws,  and  the  tubes  U.  /<' are  trussed  to 
prevent  vibration  This  instrument  w. is  calibrated  bv  aid  of  a  Wliilworth 
measurim;  machine  and  the  scale  adjnste<i  so  thai  one  division  corre- 
sponded to  one-niillicjiith  of  an  inch. 


APFI-ICATION  OK  THE  METHOD    OF    SIMPLE    COMPRESSION    TO    THE 
UKTERMINATION  OK  THb.  CUBIC  COMPRESSIBILITY  OK  MtCTALS. 

The  behavior  of  such  metals  as  wroui;ht  iron  and  steel  over  a  wide  range 
of  slrc-.s  shows  th.it  lliese  metals  may  be  considered  as  almost  perfectly 
el.istic  I'he  results  of  the  theory  of  elastic  bodies  may  therefore  be  applied 
in  their  cases  with  great  confidence. 

.\s  a  tv|)ical  example  of  the  behavior  of  such  tnalerials  we  niav  c<msider 
the  deportment  of  a  specimen  of  wrought  iron  uluii  subjected  to  a  cycle 
of  compression  stri-sses,  c  uninencing  at  i.oou  pounds  and  rising  to  (;,u(«> 
pounds,  after'vards  reluming  to  the  origin;il  load 

The  readings  obtained  for  the  longitudinal  and  lateral  strains  will  show- 
in  such  ;i  case  that  >ipial  increments  or  deerements  of  loail  produce 
strains  which  are  \ery  exactlv  i)roportional  tliereto.  This  is  clearly  shown 
in  a  plot  of  these  readings,  where  the  ordinates  represent  the  total  load  and 
the  alisciss.e  represent  strains  In  both  cases  the  relation  of  stress  to  strain 
is  represented  bv  a  straight  line  returning  upon  itself  Traces  which  varv 
bnl  little  from  the  i<leal  straight  line  are  given  by  black  Belgian  marble,  as 
will  be  seen  on  p.ige  J,s 

Such  results  atTord  an  arbitrary  standard  by  which  can  he  judged  the  degree 
of  approximation  to  perfect  elasticity  exhibited  by  other  metals  and  by  rocks 
under  similar  conditions. 

If  we  now  calculate  the  value  of  the  modulus  /i  for  simple  compression, 
since  this  is  the  relation  of  the  compression  stress />  to  the  strain  e,  we  have 

p=Ee 


ELASTIC   CONSTANTS  OP   ROCKS 


13 


If  we  cull  .4  the  cross  sectional  area  of  tlie  spednieii  when  stressed  by  a 
loud,  /'.ami  r  the  decrease  of  leUKtli  over  a  nieasiired  leiiKlh,  L,  gripped 
between  the  screw  points  of  the  measuring  apparatus,  we  obtain 

PL 


t  = 


x.\ 


which,  in  case  of  a  specimen  of  wrought  iron  examined  for  a  rangeof  S,(XX) 
pounils,  ),'ave  a    value   of    jS.  mo.ooo,  the    units    beiii);  ixiuiuls  and  inches. 
The  ratio  m  of  the  loni;itudiual  strain  to  the  lateral  strain  in  llie  same  case 
was  }i  65.  and  usinu  Ihe  formula 


1)^ 


E 


,1 '"     - 


we  obtain  for  the  modulus  of  cubical  compression  (or  bulk  modulus)  I),  the 
value  .11,  v>o,ixK),  a  constant  for  the  material,  the  reciprocal  of  wliicli  f,'ives 
the  decrease  in  volume  of  1  cubic  inch  for  1  pound  of  pressure 

While  certain  rocks,  ^.uch  as  many  of  the  inarblcs,  have  a  structure  identical 
with  that  of  wrought  inm,  most  of  the  rocks  constitutini;  the  earth's  crust 
are  composed  of  several  minerals,  and  thus  resemble  cast  iron  in  character, 
the  grav  variety  of  this  substance  bein^  .m  a>;i;r.j,'atc  of  crvslals  or  individ- 
uals of  tlie  metal  iron  (wrouiflit  iron;,  (graphite,  etc 

It  will  therefore  be  of  interest  to  ascertain  how  a  specimen  of  cast  iron  be 
'.aves  under  compression  stress,  and  how  far  its  elasticit  v  fills  short  of  that 
which  would  be  exhibited  bv  a  perfectly  elastic  boily 

!*i,r  this  purpose  a  tine  ,i,'rained  siiecimcn  of  somewhat  hard  cast  iron  was 
faced  and  tested  The  results  of  this  test  are  tjiven  in  the  following'  table, 
and  the  stress-strain  curves  are  plotted  in  lij;ure  ;,  I  represents  Icjuijitudinal 
compression  and  II  lateral  extension 

The  behavior  of  cast  iron,  .is  exhibited  hv  these  experimental  res  dts,  shows 
.1  falliiif,'  awav  from  the  theoretical  standard  of  perfect  elasticity,  but  even  in 
the  most  i)erfecllv  elastic  bodies  there  is  i)robablv  ,1  sliijht  hysteresis  effect, 
so  that  w\  are  justilied  in  usiiii;  the  results  obtained  to  calculate  the  mod- 
ulus of  compressibility,  il  the  error  intnidticecl  thereby  is  iie,i;li,s'ible  or  very 

small 

It  may  be  ijoinled  out  (hat  tills  method  .and  others  of  the  indirect  type  have 
been  freelvused  to  obtain  values  of  the  liulk  modulus  for  east  iron  and  metals 
of  like  character,  and  it  will  be  shown  that  the  composite  crystalline  rocks  are 
very  similar  to  cast  iron  in  their  behavior  under  stress,  although  generally 
more  perfectly  elastic. 


8 
% 

\\\ 


•4 


AN  iNvi;>ii(i.\Tin\  iNTii  Tin; 


I  u-i  /,, 


Sl/.- 
Aril.. 


I     1141 
1  •■  (HMHHH 


I  "nKilii.lin  il     (■■minis. i, ,„     „,u|||,,iy    ri.Kliniis 
t»V  4    f'T   iiiilliKntliM. 


I.ua(J  lin  [Hiundb). 


1  ,<XX) . 

I.IKX) 
t.lMKJ. 

>,(XK). 

:.tx»o 

<,CK10. 
».(XK>. 
\1)1K) 
■.(KKl. 
I, (NX). 
;,INX). 
I.IXXI. 


Side 
P. 


<9 
4" 
fHJ 
So 
lex) 

I  ..'O 
I  ID 
llil) 
lis 

!-'« 
104 


Sidi- 
V. 


37 
58 

7,s 

K)0 

'H 

['■11 

'43 

1  -■  i 
I  10 


Liiti-rul  extt'tisiim— 

imillitmttiK). 


Side 
i'. 


JO 

21 

4> 

>S») 

3  J 

><3 

III) 

iir. 

imi 

lo.-i 

1)1) 

7" 

'id 

lin 

-II 
(11 

Ml 

-•1 

Kidc 


5   TRAIN 


l-tG.  3. — Cast  irim      Strcss-slniiii  mm-. 


Kr.AsTIC    Cii.NVrANTN    (IK    KUCKS 


APPLICATION    OK    THE  MKTHOD    OK    SIMPLE    COMPRKSSION    TO    THE 
DKIKKMINAIION  OF  TllK  COMPRESSIBILITY  OK  KOCKS 

It  li  I-  l..'.n  n.,t(.l  ni  ilir  .MM-  ..r  iii.irl.U  wli>  ■  Mihjivlr.l  to  tHtidiin,'  >lri>.s 
tli;.l  Ih,  -lr.Mii.,s,Aliil..i.-.|l,vtli,Mk.||>fli.m.,i  ..Mil..lllu.lMrinma.rs-.v,  >! 
the  time  iii.l  iIk'  sin  ii,.tli  iiii  I,  r  .lir.r  pn.  Im<-,i|  hv  ,i  t.,n|iK.  w:i^als.)  I.mim.I  t.. 
hc-i.,  Muall  tint  ,1  .l.lrniiiii  ,li,,„  ,,1  ilu-  slriiTi  «a>  v<rv  (lilliinlt  I..  tneuMin- 

'1  hoi'  iliirKiiIlii-,  h  tw  luni  umnl  hv  N.i-.ink.i.*  wIm  slai.s  thil: 

l>rvliiMi»;,rv  .■xiKTiin.nt.cti  ^r„iii<-  .li,,»  tl,,,i  ri.,.,k,.\  |,,„  .|..,.srM.|  Imlil  .-vvn  for  vt-rv 
small  lU-xi,r,.  ,,n,l  i.-hm,.,,,  .,n,|  ||,.,I  ,1,.-  ,,IIit  i  llVrt  K  wrv  .■,.„si,|,.r,,l,k.  fr.,m  ||„.  pressure 
«-lK-„tl,..  ,,r,„n  iss„liUu„.lvl.,,„l,..|„r  , » j.u.l.  ,1,..  ,|,u,„i,„,  ir,.,„  ,!„.  .lir.ct  i.r.'|.or.i.,„-' 
..li.v  l,.i«..i.„  s,r.,iM  ami  s,,...,  „.,s  „k-o,„,,  ,ral,lv  ,„  „  a.  oMnparv,!  v.i.l,  that  oLs^rvi.,! 
"1  Mutal  I  his  nnis,  l„.  .  |,i..||v  ,I,k.  t..  t'u-  l..«  1,„mi  nf  ..laMi.  itv.  „,  ,!,:„  „  i,  n.ves^arv 
f.  ex|K.riMU.„t  „nlv  w,il,i„  very  narr,,w  linui,  ,,|  l„a,l,„K  a,„l  uvis,,,,,..  iU,.,-  lj,„its  are 
«iclclyHini.r<ail  Inr  .lillVri-nl  -,|„cimeiis  .,f  r..,-ks,an.|  ihf  m..J„l„s  „f  .laslidtv  ,s«dl  as 
Hut  of  n^„luv,  „„.  ,,hvavs  .I.-.frmiinal  «i.l>  s„.-h  s,».s,es  as  will  a|,,.r..xin,atelv  ,.ro,l,H-c 
strains  proporiioi.ai  ,o  ,Ik.,„  ||,e  ,leviatin„  fro,,,  ||o„k.',  law  was  pro,,,,',,.,,,  i„  ,,.,,,,i„ 
spiT„„e,is  of  samlMoiK-.  ami  it  was  ,nor.-  ,„arkc-.|  i„  t.asio,,  tliari  i„  ,l,.x„ri.  cxiHTiincnts 

Ml  ivriain  roots  I.  is  i,„k.iMl  ,lo„l„f„lir  anv,l,i„,.  lik.-  a  pr .,  li..„alit  v    hHw.en  stress 

an,  Mrain  can  Ik-  fnnn.l,  .  vt-,.  for  cxir.andv  s,„a!I  rlian^,.  of  s|,a,,v.  i  mi  la-U-asin.-  tl,i.,e 
r,H-ks  fro,,,  s,r.-ss  ,|,,  return  toward  tl,..  fortner  slate  i.  ext,..„,e!v  s,„all,  .l,owi„,.  .n  „  ,  |„. 
elasttcir.  "f  ihe  rock  is  of  a  very  inl.rior  or.l.r. 

These  ..l.s^TVutions  of  \a:,M,)k..  lor  lumlin-  and  twistiii-  have  Incn  con- 
liriiuil  by  our  own  .Ullci-liou  .xiHriiiu  nis.  as  ahovt-  iii.iili..in-,| 

If,  howcvr.  tlR-  rock  lu  sul.itTt.d  to  uinrt  i-o,„,,r.ssioti.  strains  in  wliid, 
t  K'  tune  elTcc-l  ts  stnall  and  the  la-of  thfstrai.nsalsosn.allareahip.st  invari- 
al)lvol.ta,ned  fhisis  csiKciallv  tlie  ease  if  before  the  aelnal  experiment  is 
earned  ont   the  niaterial  be  several  times  stilijeeted  to  a  ranLre  of  stresses  at 

preliminary 
IS  also  eonimonlv 


least  as  -real  as  those  emplovcd  in  the  experiment  itself      This  prel 
stressiiii;  brin.;s  the  material   to     'a   state  of  ease,' 
adopted  when  the  elastic  coiislants  of  metals  are  d 


It  is  evident,  therefore,  that  this  direct  eomi 
fulence  beapplied  to  lh<-  mi.  i.;tiroo,,.  .t   ..i-  .i.. 


letermined 
)ression  method  m: 


vith 


although  as  mentioned  bel 
with  dilTereiit  classes  of  rocks 


e  I'leisiireine  It  of  the  cubic 


low  the  accuracv  of  the  result  so  obt 


cotiipression  of   rocks 


lined  \vi 


lldifTei 


If  the  rock  be 


be  safely 
the  rock 


employ 


massive,  eompact.  ami  cr\  slilline  (orghissv)  tli 


ed  and  j;ood  results  will  b;  obtained       I 


rs  seliiitosc,  porous, 


le  method  ciin 
f.  on  the  (ither  h.ind. 


nature  of  the  case  be  very  miicl   less  satisfaclorv 


)sely  coherent,  the  method  ,vill  f 


roni  the 


The  plutonic  igneous  rock 


in  structure,  beins  holocrvstalline  and 


s  .IS  a  class  most  iiearlx 


resemble  the  metals 


lassive,  and  therefore  i)resent  tli 


Mag., 


♦Klastic  Constants  of  Kock 


vol.  L,   1 


yoo,  p.  5t( 


ocks  and  tlie  Wlocily  of  .Seismic  Wavt 


H.  .\;, 


I'hil. 


m^^&yiM' 


ift 


.W    IWICSTIC ATION    INTO    TIIK 


lUMPsI  .i|)|)rM  u'h  jniMll,;  nuk-.  In  pi  rl'ifl  il.isliiiU  ;  llirv  lire  ltirrtf<irr  ;i  cliiss 
"I'  rc'ik^  liiwhirli  iliis  tmllin.l  is  i  spiiiallv  :ip|ili(;ililf  M  lurliiiiiiU  Iv  liappciiH 
tinl  llii\  iir  .ilvi  .1  <l  I,-.  Ill  rnvk-.  ;i  kiii>vvli'<l;;»' of  \\  Imsr  idiiipnssihilitv  is  iif 
spi  .-i  il  imp.  ■rl.iiK  f  I'mi'  llu  ilihi(|;iiiMii  (if  iii;iiiy  K>'"'l"xik  il  pmlilciiis,  nmsl'tiil - 
l.ii;  .IS  Iticv  111  tin-  i;i.   iliT  p:!t!  iif  llu-  c^irlll's  crilsl. 

A  sioiiimI  class  iif  riifks  vvliii  h  arc  lunip  aralilc  willi  lluiii  in  lliiir  appn  Ii 
In  pirfci-l  ilastii'itv  t  iinprisis  llic  in  irl)Us  ami  iirlaiii  liiiu  slums 

A  sirii'S  'if  sj^inii  t\pual  rmks  ripnsciilativf  i>f  tlii-si'  two  classts  were 
ai-,'irilin.;lv  silicli'l  lor  imasiiriiiuTit  I'mlir  llic  first  class  a  iiuimIht  nf 
ijriiiilcs  were  cliosiii  IS  nprcsi  iiiiiij;  ilic  aciil  pliilmiic  mcks  ami  a  iiiiinlicr 
of  Ivpcs  nf  tlic  Kahbrn  cssixitc  scries  were  sclecled  as  reprcsciilini;  the  basic 
philntiic  rucks  III  all  these  cases  L;reat  care  was  taken  tn  clinose  the  nmst 
hnTnnL:enenMs  ami  ma  sive  nicks  of  eacli  st  ries  and  tn  secure  test  pieces  free 
frnin  all  llaws  ami  c;  icks  As  n  presiiitiiii;  the  sicnnil  class  a  miinlHi  nf 
typical  inarliles  ami  lini'^lnms.  also  pirfu'lh  massive  in  i  li aracter,  were 
srlecled  I'or  pinpnsis  nf  cnniparisnii,  or  cnnlrast,  a  sanilstoiic  was  added 
tn  the  list  as  luini;  a  mck  which,  mi  accniinl  of  its  imire  or  less  porous  iiatiiri' 
caild  hardlv  he  e\[iectcd  to  vield  salisfaclorv  results  hy  this  niilluid 

An  c\aniinalion  of  the  stress  strain  curves  of  t'ase  ifi  rocks,  oiniltin^; 
the  sindstoiie,  shows  that  on  the  averai^e  Ihev  possess  a  rather  more  perfect 
elislicitv  and  exhibit  less  hxstensis  than  cast  iron  Some  of  them,  as  for 
instance  the  lia\  eiM  ,'r mile.  I  he  n']ilieliMe  svi  uite,  the  diabase,  and  the  black 
Iieli,'ian  m.irble.  show  much  lietler  curves,  approximaliu!,'  in  fact  to  the 
straiijht  lines  i,'i\  en  b\  \m  .U'.;hl  iron,  which  may  be  considered  for  our  present 
purpose  as   exprissiii^'  perfiil  elaslicil\ 

The  close  approximation  to  perfeit  elastieitx  is  shown  b\  the  relnrn  of 
the  curve  to  its  initial  or  siariiii:;  point,  and  the  amount  of  the  lusteresis  is 
shown  bv  the  widlli  of  ihe  loop 

The  width  of  this  Insteresis  (or  kit;*  curve  or  loop,  imlicitis  theaniouut 
of  the  divir^'eui-e  from  Hook's  l.i  .  wliiih  the  material  exhibits  this  law 
beini,'  that  the  stressand  strain  are  •liially  proportional.  When  the  curve  is 
narrow,  as  it  is  in  aP  cases  except  the  Statistead  ^wilc  and  thes,indstone, 
the  diver.:iiue  from  Hook's  law  is  not  ^'re.it  enoui;h  to  seriously  alTcct  the 
resnll 

'llie  rocks,  ihirefore,  with  thest'  exceptions,  fulfil  thecnnditioas  of  elastic- 
ilv  luccs-  ir\  to  the  siucessful  application  of  the  method  In  these  twn  cases 
the  risulls  arc  less  certain,  owinij  In  the  ijreater  hvsteresis  of  the  rock 

It  mii^ht  at  first  si'j;ht  ap[)i>ar  tint  while  the  luethod  emplir,  ed  is  tiieorelic- 
allv  prrl'eci  I  applied  to  the  imasuremenl  of  the  conipressibilit v  of  vilreo-.is 
rocks  and  of  verv  fine  '.^'raiu'-d  crvstalliue  rocks,  a  considerable  error  iri.ijht  be 
inlroihiceil  wluu  the  rocks  are  co.irser  in  ;;raiu  In  the  case  of  all  the  com- 
mon crystalline  rocks,  the  individual  grains  of  which  the  rock  is  composed 


KI.Asm       .INSTANTS    <  <V    «i  n.  KS 


\ 


arc  anivilropic.  tli,,i  is,  \U,y  Imv,.  .lilT.  r.til  iihMhili  of  .l.isii.itv  in  .litT.  r.iit 
flinrlintis  IntnisMv.-  PH-ks  mh'Ii.isIImsc  iiiv.sti;;,,i.(l,  ln.w.vir,  tlicsc  uniiiis 
occur  ill  the  nek  'Aitli  i-i  i.livihil.lv  irnijiilir  ..riciil  iti.m  :iii.l  w.mld  in  the 
case  111  a  line  •^'raiiie  I  rmk  i:imIii  illv  ciimi«iisate  fur  (me  an<tliiT  in  any  trans 
Vfrsc  line  al'in-  wlii,l,  the  exp.iMsi.m  .i|  the  mek  tm.le,  -.mipressinn  m'lKht 
be  Mleasnreit  ll.  h.uvever.  the  r-uk  were  c.irMr  in  i;r.iin,  fewer  iniliviihial 
crystals  w,,til,|  !„•  f.iiinil  in  anv  Iransverv-  line  of  s.rliuii.  anil  there  ini;,'ht 
possihiv  in  this  ua\  he  a  lack  nf  ciiniMiis  iti.m,  as  the  rock  in  one  s.rtilm 
iiiiKht  lie  compos, (I  of  grains  whose  axis  of  ^-realer  elaslieitv  approxini;ite<l 
on  an  averaije  more  luarlv  lo  th,.  ilirection  of  .n.asiireinent  than  in  other 
•sections  If  such  were  n-illv  the  case,  there  shoi,|,l  Ik'  In  thes,-  eoarscr- 
Kraineil  rocks  an  exceplioiullv  ureal  vari alion  in  the  reailin„'s  olitaine.l  from 
dilTcrcnl  specimens  of  the  same  rock,  a .  well  as  fr  ,in  the  ,li(Terent  sections  in 
the  same  specimen 

Milt  such  is  not  the  case,  as  will  he  seen  hv  all  ey  imiiialioii  of  the  ti;,'ure 
accompanvini;  lahle  Thev  represent  the  results  ohlaiiicil  from  ten  luea; 
inents  o;  the  compressihilitv  of  Havcno  .granite,  which  is  coarse  in  j;rain.  ,  I 
ten  of  Suilhurv  .li  iliasc.  which  is  ver\  line  in  j;rain,  together  with  ciKht 
measurements  on  Tennessee  limestone,  which  is  ratliercoarsei;raiii,  anil  seven 
on  plate  jjlass  They  were  made  in  eachctse  on  two  or  more  specimens  cut 
from  the  same  mass  and  the  measurements  of  the  expansion  were  made  on 
several  dilTerent  planes  throm;h  each,  so  that  in  <  vervcase  the  measurement 
was  cITectcd  in  a  dilTerent  line  throu-h  the  roek,  all  of  these,  however,  of 
course  heiii;;  at  riuht  ani;les  to  the  direction  of  the  compressive  stress  and 
lyini;  in  the  medial  plane  of  the  column 

Full  details  con.eruiie.,'  each  tneasnreiiieiit  will  he  found  in  the  tables 
which  set  forth  the  results  obtained.  luitUr  thesecl  ions  de.ihn- with  the  several 
rocks  ill  ipiestion  The  si/e  .1  i^raiii  and  the  texture  of  the  rock  can  also  he 
seen  hv  ex.iiuinin-  the  ph  ■  aicro-raphs  and  color  prints  of  the  ix.lished 
surfaces  of  the  res|)ec(ive  rocks 


Max. 


Min. 


Diir. 


4,.SSO,CKX> 

4. 

V*^O.OIHt 

Srio,cxx> 

1  t.  I7o.n<v 

1). 

OSS.'Mio 

I.il  i,i»») 

'"'.V.^o.lx.io 

''. 

IJO.IKKI 

>lIO,IMK1 

'M  io.'Hio 

.S, 

7;il,IKH> 

,U">,o<X> 

Hnvetiii  Kranitc   (cnafM'i  ii>  tritis     

Siiil'iurv  (lialiiise  (very  liiu-l  m  iri.ils 

f' .  .'  Klass,  I.!  trials    '     

Tennessee  inarlile  (ralhir  OKirsei  7  trials 


It  will  thus  he  seen  that  there  is  no  correspondence  between    the  coarse- 
ness of  Rrain  and  the  maKuitmlc  oi'  the  variations    in  the  readin-s  obtained 
The  differences  in  ,'1  iss.  which  isau  isotropic  material  in  which  the  elasticity 
is  ei|nal  in  all  directions,  are  greater  than  in  the  Tennessee  aiarhle,  whi-'i  is 
rr.ther  coarse  in  i;rain.  and  in  Baveno  granite,  which  is  the  corT—'-  ..■■  '-- 


i8 


\N    IN\  liSTIC.ATKlN    INTi)    THi; 


tin-  --rt        riir  :;rc;ilc^l    dilTcniux'-  nlitaiiicd  ;irc  lliosf    fotiiul   in    tlie    finest 
nr.iiiKil  riK-k  in  the  si-rn  -.  \  i/.  tin-  Siidhnrv  dialM^cv 

It  is'vickiit.  Ilunlnn.  iliat  tin- (lillVniit  nKJihili  of  clasliiily  (.f  tlu' tonstit 
niiit  L;rains(ii  ,i  nuk  (1m  mi'I  iiilmihu^'  an\'  ]iiT(.-cplil)U- iTmr  in  nii-aMiri'inents 
iiiaili  li\  tlii>  nitlliinl.  win  n  a  inlunni  an  iTii-li  in  dianuur  is  tnipliiycd.  and 
ulna  llii-  locks  arc  n.il  i-narsir  in  ,^'rain  llian  tlic  liavcmi  ,i;raiiitf  In  fact, 
uliilc  surrmnidid  mi  all  sides  In  iUhcr  ,i,Tains.  no  iiu'iNidnal  ),'rain  can  cxjjand 
fnch  .a-,  it  \Maild  if  snUjiclcd  to  i-oniprcssion  nidia  iip'.rcd  by  any  snrnunidinR 
incdinni.  and  tlms  llf  anisoiro|)iccliaracUr  of  ihc  indi'  idual  ;^'rains  prodnccs 
but  liltlc  cITccl  o.i  l!ic  clasiuitx-  of  the  rock  as  a  uliolc 

Tlicsc  cNiicrinicnts  also  skiw  that  in  llu-  case  of  rocks  composed  of  several 
minerals  it  makes  no  |nrcepli!ile  dilTerince  wlietlicr  tlic  points  of  attach- 
ment of  the  instrumeiii  are  eiiihedded  in  llu'  ^'raiiis  of  one  mineral  or  of 
another 

The  cliiif  sonrcc  of  error  and  the  one  to  which  tlic  variations  observed  arc 
for  Ihi-  most  part  to  bi'  ;■'  iilmted  seems  to  be  a  mcclianical  one,  viz,  the 
diHicuU\  of  ■^(■1  till i;  an  id.al  contact  belwi  I'li  these  points  of  altachineni  and 
the  spieinuii  to  ire  nu  astired.  especi,dl\  in  \ie\v  of  the  extremely  small 
dinnnsioiis  of  the  movement  to  be  ineasnred 

■rhei|uesliouof  iluinlhienceof  temperature  on  the  elasticity  and  compressi 
liilit\  of  roi-ks  is  of  conrse  one  which  has  an  important  bcarini;  o!i  certain 
problems  of  ■jeophvsics  TheoidN' invesli,;ationof  this  snbicct,  so  I'ar  as  can 
he  asecrliined,  consists  of  a  few  preliniiuar\  exiHiimcnls  In  N'aj^aoka  and 
Kas,ikal)e  *  In  Ihesi'  the  torsion  melhoi]  w;i>  employed,  and  the  experi- 
ineiiis  wi  re  eirrieil  out  on  a  sim;!e  rock,  viz,  s.mdstone  This  rock,  as  has 
alreadv  bicii  mentioned,  bein^;  porons  and  stnitil'ied  in  character,  is  a  material 
whose  elastic  properties  are  far  from  ideal  The  results  are  summed  upbv 
the  authors  in  the  following  words: 

l'reliniiii,ir\'  i\jh  riiiuiil  s  wiili  s;m,Isii.Mf  s]i<i\\  llinl  tlu-  inn. lulus  t>f  cKisticitv  is  luucll 
a!Tei.t(  <1  i'v-  1  lie  \  it  i  il  imi  i>i  t  rinptT't  n;  <■.  ;  i  ,  ;!..iul  o  :^  per  ecTlt  periU".:ree  It  il'tes  fli-t, 
lidWfM  r,  ut  i-e  •-  nil\-  ili'iiMu^lMv  if  li  i  lie  inerei'*-  "1  tt'iii]nT;il  are  where  tlie  leuipcT.Uure  is 
lew,  J   ,  .  ii  is  111  txinmni    iL.iiit  >)    ^" 

.\s  h,is  lueii  shown  liowi'Vir.  the  values  for  the  elastic  constants  obtainicl 
bv  this  I  ision  and  luiidin;,'  iiiethtid  have  vielded  results  whicli  can  not  in  all 
easi'S  ln'  correct  and  uhich  dilTer  \  er\  cotisiderabU  fmm  tln'se  obtained  bv 
the  miife  dirit'l  and  simpU'  nuthod  which  has  been  emplo\((l  in  tin  present 
p.ijier  These  results  bearing;  on  tl'.e  vari,ition  of  ilasticit  \  induced  b\  diailKcs 
of  temi>eralnri',  especialh   in   \  iew  of  tln'   fact    that   tlii\    are  stated   bv  the 


*M  uluhis  of  I';i.ist  icily  of  Keeks  Line  1  Wloeities  i>f  Siisniic  Waves,    ruhlicalions  ef  the 
l.aillii|iKike  Invesligalicii  Coniniillie.    No.  17.     Tokyo,  1904,  p.  43. 


KLASTIC   CDNST.WTS  OF   ROCKS. 


IP 


investigators  to  hf  "proliininary, "  can  as  yet  hardly  be  taken  asof  general 
application  toallnnks,  even  if  correct  lor  tlie  specimen  of  sandstone  exaiiiin'd 
In  our  own  in\csliL,Mtions  the  laboratory  wis  maintained  at  a  ttinpiratiire 
of  from  ()f  to  (),s'  1''  (i;  j-  to  20°  C  ),  and  a  tlioroii.i,di  iiivc^tii;ali(iM  into 
the  effect  of  tempt  lal  lire  nas  not  iindrrlaken.  as  this  would  be  \  <r\  difluidt 
to  carry  out  ulu-ii  eiiiplo\  in:;  the  nutliodof  direct  compnssioii  '.ised.  tin  <liHi 
ciilty  consistiiii;  in  heatiiij;  the  S])ecinien  itself  uiilidiit  in  am  \\a\  atT((liii<,' 
the  ineasurini,'  apparatus  attached  to  it 

It  seemed,  however,  possible  to  a-.cei  I  lin  wlivlheraiix  serious i'han<,'e  in  the 
elastic  constants  of  the  massive  ervslalliiie  rocks  emplo\-erl  in  the  present 
investiifation  would  n-sult  from  a  moderate  cli;niL;e  of  temperature  l"or 
purpose  of  trial  tliemeksekcted  was  the  .Snrlbiirvdi.iliase,  a  t  epical  line  ijrained 
plnlonic  rock  .A  column  of  it  was  placed  b\'  Mr  McKer;,'ow  in  1  sm.ill  list 
iiii;  macliiue  haviii:;  a  eapacitv  of  ,so  tons,  and  the  temperature  of  i  in-  looni  iii 
which  the  machine  was  set  up  havini.;  been  lowered  to  1-  10'  I"  .  a  evele  of 
compression  readiii'^'s  were  laken  in  tin-  iwual  w,i\  a  lopied  win  11  N'iiaMi,''s 
uiodillus  is  to  be  determined  The  teiui)enitiireof  llu- room  was  lluii  raided 
b\-  about  10"  and  aiiotluT  evek'  of  re.nlin^js  win-  taken  It  w.is  llieii  riised 
another  10"  and  a  third  series  of  readiiiL;s  were  obtained,  and  so  tliroii;;li  sue 
eessive  Staines  of  10-  until  the  normal  temperatureof  the  room  (about  fi.s'  I"  ) 
was  re.iched  The  inili.d  re.idiu','  of  the  inslrunuiit  before  tin-  apj)lic.ition  of 
pressure  wasof  coiirsedilTereiil  in  each  case,  owiii:;  to  llice\p:iusioii  of  tin- rock 
which  frillowed  from  lu'atim;  These  initial  points  were  |)loileil  on  a  liiU'. 
and  the  results  obtained  when  the  speiinu'U  was  subjected  lo  a  i-trtaiu 
tnaximinn  load,  tO'.;etlier  with  the  iuen'ase  of  temperature  at  e.uh  slaijc,  wrre 
plotted  on  a  second  line  If  thccompression  wasi;realer,it  65"' tli  111  at  10  f.ir 
the  same  load  these  two  lines  shoiilrl  have  diveri;ed,  but  as  a  m.itler  t)f  fad 
they  were  practicalh  parallel  Thedifferences  bet  ween  th<' reading's  i;i\eii  b\ 
thesamelo.idat  difFerent  temper.itures  were  no '.,'Rater  than  those  obtained  b\' 
different  uieasiirenieuls  uiidi  r  tile  same  load  al  Ihi' s.nue  trmper.iliiri'  Tlu' 
conclusion  therefore  seems  to  be  iiiilicated  that  1  eliaut;eof  temperature  m  ide 
110  percei)tibledilTerence  within  tlieranj;eof  temperatures  cuiploved.  although 
a  dilTerence  of  o  5  ]>ereent  l"or  each  dei;ree  ceiltii,'rade.  wliieli  a:is  \a;.iok.rs 
result,  would  mean  .1  dilTerence  of  about  :!.s  per  cent  in  rait;;e  of  temperature 
eniploved  bv  .Mr   .McKeri^ow 

While,  therefore,  this  experinunt  cannot  beconsidered  as  siip])l  vim;  accurate 
information  coiicernini,'  the  effect  produced  b\-  a  risi-  in  temperature  on  the 
elasticcouslantsof  rocks,  for  theinstruments  tluniselvesare  in  some  measure 
affected  bv  the  same  chaiises  of  temperature.  tlie\-  serve  to  show  th.it  in  the 
CISC  ol  the  m.issive  ervstalline  rocks  tlu'  inlluenceof  temperalure  is  piobablv 
not  very  i;i-eat       I'he  subject  is  one  which  reipiires  further  iu\  esii^MtiiJU 


.<^;''.,:rf'  , 


-30'    ViWE».«   1..    '     W«»P.i 


Pmii 


AN    INVi:sTI(;.\TI(IN    INTO    TIIIC 


THE  METHOD  OK  MEASUREMENT. 

Ill  iMrr\iii^  iJiil  tluTiicasurriiuiils.  iirisins  nf  the  rmk  apprdNiiiuilcIy  i  iiu-li 
S(|iiarr  and  ;,  iiR-la-s  Imit;  ucrt-  iisiiallx'  ciiiplcyid  (sii-  li;;  4).  'riu-sc  were 
iMit  and  ,i;t"!iii(1  w-lli  siiinotli  faas,  but  uiro  11., t  piilislu-d  In  Uusi-  two 
Miiall  nnnid  Imlis  \vcn>  drilkd  in  tiii'  imdial  liiii-  <>i  ladi  vertical  I'licv  for  tlic 
purpose  ,,i'  attaehiii^'  the  iii>lriiineiit.  when  \'oi:ni,'s  uioilidiis  was  to  he 
measured  Tluse  holes  uere  made  l)\  means  of  a  small  diamond  drill  and 
Wire  ]Hrfeetl\  r.iniid  and  sm.ioth  The>  were  eaeh  00s  to<MiS  ineli  in  dia- 
meter and  o  i.'s  iiioh  deep  and  1  j.s  iiiehes  ajiart,   Ivini;  at    e(|nal  distances 

al)o\eand  below  the  center  of 


5 

\ 

I 
3  mm. 


Detail  of  hole 


Hole 


■J 


the  prisms  These  holes  were 
chamiifered  at  the  ontir  end, 
as  shown  in  fimire  4,  and  were 
found  to  alTord  the  inirst  per- 
fect attadinient  which  eonkl 
be  secured  lor  the  points  (jf 
the  instrunu  lit  Hv  means  of 
these  prisms  two  sets  of  nieas- 
nrements  of  the  vertical  com- 


'^   '-^ 


I'l'.     (.      Sqll  ire  Ii-l    --peeillletl  ..f   ii.ek. 


I'lO.  s.      kciuilil  test  s|iceinieii, 
sill. will-  |w.sniiiii  ,.f  holes. 


pressj.-;  emild  be  made  with  each  prism,  b\  altachini;  tlu-  iiistrnment 
lirsl  to  one   ]iair  .if  uppusite  f.ieis  and  then  to  the  otli<  r 

111  sr)me  <Mses  round  colmniis  weri'  used  (se<-  li','.  i)  These  wire  approxi- 
m.iiel\  I  inch  in  diameter  and  ;  inches  in  leiiuih  Willi  lluse  it  naspossible 
III  make  four  s,  ts  i,{  nii  isiireiii, m  s  in  cmpn  ssii.n  w  i'.h  i,>cli  column,  In  drill- 
in:,'  ei:;ii  I  ))iirs  i.f  holes,  as  abive  de,erilieil,  \i  ii.we  planes  intersected  at 
anodes  of  45    iusie.id  of  01  "  as  in  the  si|ii:ir,    prisms 

It  was  111  enurse  uecessar\   in  e\  ei\   i  ase.  w  hi  tliir  prisms  or  Columns  were 

er) 


ELASTIC    CONSTANTS    OF    ROCKS. 


o 


carefully  faced  and  absolutely  parallel  to  one  another  Refore  the  actual 
measurements  were  made,  the  rock  in  evervease  was  hrnujjht  toa  "stale  of 
ease"  iti  the  niamur  already  deserihed 

The  pressiiri'  uns  apiilicd  in  most  cases  hv  a  luo  ton  Wiekstead  tcstini,' 
machine,  which  was  so  carefully  adjusted  that  it  was  sensitive  to  a  load  (pf 
4  pounds 

Thespecimen,  ha\  inijbcen  placed  in  the  i)ress  and  reduced  toa  stateof  ease, 
was  then  after  careful  adjustment  submitted  to  loads  incre.isiuj;  in  successive 
sta^'es  of  r.ooo  iiounds  until  the  liniil  of  su\'t\-  liad  been  reached,  when 
(he  load  was  reduced  successively  bv  the  same  aiuounls.  accurate  readings 
beins;  taken  at  each  increment  and  decrement  of  load  The  maximiun 
load  emploved  in  the  case  of  most  rocks  w.is  ij.ooo  pounds,  e(|uivalent  to 
from  <),()()(>  pounds  to  about  11,500  pounds  per  scpiare  inch,  accordinj;  to 
whether  a  sfjuare  or  round  prism  was  cTUploxed  In  the  case,  however,  of 
some  of  the  stronger  rocks  a  load  of  as  much  as  15.000  pounds  pir  s(|uare 
inch  was  enqjloved 

In  the  determination  of  the  lateral  strain,  which  was  Tuade  upon  the  same 
set  of  eohunns  as  those  use<l  for  measurins;  the  v<-rtieal  couiiiression.  e.ire 
was  taken  that  the  theoretical  eoudilions  were  r<'ali/ed.  and  thai  the  nial<  rial 
was  free  to  expand  lati-rallv.  as  otherwise  the  values  obtained  for  the  laleral 
extt'iision  Would  be  inaccurate  In  all  casis.  therefore,  llie  meiisurini;  a;'pa- 
ratus  was  set  as  nearly  as  ])ossible  upon  the  central  section  of  the  test  jjieee, 
and  the  ends  of  the  specinun,  after  beim,'  !,'rotnid  smooth,  were  coated  with  a 
thin  film  of  oil,  so  that  the  polished  pressure  plates  of  the  ni.ichine  would 
have  as  little  teiidi-ncy  as  i)ossil)le  t'l  ])re\aiil  freiilom  of  hiliral  expansi.ai. 

In  a  inunber  of  eases  aeenratt'  measurements  were  lakin  durini;  tlie  sue 
eessive  cycles  of  luadiui,'  and  unlo.idiu,'  to  which  tlie  spceiuien  uas  subieete<l 
in  order  to  brin:;  it  to  a  slate  of  rest  Tlu'se  nvv  recorded  in  the  e.ise  of 
the  liaveno  i,'ranite  and  :  -stansieail  i^ranite  and  serxid  to  show  how  the 
hvsteresis  of  the  rock  ma\  oe  r<'(hu-iil  to  a  Hiiniuuun  b\  subiniin;'  IIk  lest 
piece  to  this  process  The  me.isun  lUeiil-  oi  cin-h  ev.le  usiialh  oei  iipicd 
from  10  to    I  5  mimiles 

It  was  at  llrsi  conjeelured  that  in  the  ease  of  roeks  c. imposed  of  se\cral 
minerals  dilTerences  of  readinj;  mi;,  .1  result  from  the  allai'hment  of 
the  extensometer  to  difTenail  portions  of  the  ri>ek.  Ilie  points  of  the  inslru 
meiit  biini;  fixed  in  some  casesin  ,t;rainsof  one  inineraland  in  oilier  cases  in 
),'rains  of  another  It  was  found,  however,  as  has  alread\-  been  mentioned, 
that  themeasuremeiitsi.il  two  sets  of  prism  faces  made  in  Ihe  maimer  ab..\e 
described,  or  on  the  four  planes  interseelim;  thexerlieal  columns,  where 
these  had  been  provided  with  eit;ht  pairs  of  holes,  showed  tlKit  in  Ihe  case 
of  the  rocks  examined  the  differences  between  the  several  nuasuremi  tits 
oil  the  same  prisiu  ;,eein  to  be  imaiTected  by  the  eiicumst.iiiee  al/.m-  nferied 


W    INVI.'.-TK.ATIiiN    INT'i    Tllh 


to  Till'  ilifftioiu'is  hi'twciii  llic  iiR;isiiriiiiiiits  thus  iiiiulc  on  rocks  composed 
of  scvira!  iiiim  rnls  were  no  >;n  iiter  tliaii  lliose  round  in  tlie  ea>e  ol'  the  linic- 
>lones,  uliieli  were  e'iMjiioseil  cif   ilie   -^iii'^li-   mineral   e.ileile.  or  on  i,'lass 

In  tile  ea^e  of  llie  ina  joril  \  i  if  I  lie  re.eks  iii\eslii;aleil,  a  niirnlur  of  prisms  or 
eMhiuiii^  eiil  fi.  an  I  he  same  lil.  lek  of  n.(  k  U(  ri'  measnri'il  in  onler  lo  aseertain 
vvlulhi  r  (lilTerelil  tesi  pieei  s  \\oiilil  ,i;i\e  iili-nliial  reailim;'^  ll  was  foiuid 
as  a  ri^iill  of  ihesi-  i!i\a'sti:;alions  thai  the  ilil'fueuees  In  twe<ii  the  ililTereiil 
speeitiieus  were  no  ;,'realer  than  those  whii'h  were  olitainid  li\  measuriui;  tlie 
same  speiinuiis  witli  the  inslnmieiit  altaeheij  at  cliffereiit  plaeis  III  llie 
ea-.e,  lioweeer.  of  the  (_>nine\  i^ranite,  list  jjiei'is  from  two  dilTirent  hloeksof 
the  roek  u  in-  ])iepan  d,  and  it  was  I'oinid  that  while  the  several  miMsnremeiits 
made  on  eaeh  test  ))ieee  aL^ieid  anioie^  t  heiiiMl'.  cs.  there  was  a  di^tiliet 
ilieer^'enee  in  the  elaslii'  (on^lanls  of  tin  two  ■-peeiiin  lis  of  the  r<iek  This 
\\as  |i.-.ilialil\  due  to  a  dil'fiteiic.-  in  eomoc  isitimi.  as  the  two  rocks  dilTered 
SI  iuu  what  In  appe  iianet 

la  the  ia--e  of  the  -leeii  L;alil>io  from  \i  w  ( '.las.jow  .  the  re-^iill-.  olitaiiu  d  In 
mr  i^nienu  ii's  made  upon  dil'fereiit  pirKof  ilusame  pri^m  wire  diseordaiit. 
for  Ka^iiis  which  will  I"  poiiiOil  out  and  which  were  di  aleiil  upon  the 
^truelure  ■  if  the  roek 

I'iflv  ll\a'  si)ecinH'iisiif  rock,  iiiiu  Inn  of  -las^,  and  two  of  iron  wereeiu]i|ii\  ed 
in  this  Investigation  and  e\cr\  conceivalile  pieiMulioii  uas  taken  toiiisnri' the 
attaimiKail  of  leenrale  re -lilts  I'lu  roek- in  all  case  ■.  wen  airdr\ .  liavint;  been 
allowed  to  remain  in  the  Ialioi,iior\  for  -.e\eral  vMcks  aftir  the\  had  heen 
cut.  In  fore  the  me  i-nreau  nt  ■  w< n   m  iih- 

In  tile   ac.-onipaii\in,'   tallies    the    followiii'^  elastic  constants  arc   ijivcn: 
/■•       ^'■lllll';■■s  niodnhis,  I,  ,  llie  ipioiient  of  the  longitudinal  stress  l>y 

the  liiii,;ilndiiial  compression 
-       I'oi'-son's  Ratio;   this  i^  the  reci]iroeal  eif  m. 

IJ       .Modulus  of   Culiie  Compression         /  ) /■."       The   reciprocal 

of  ihi-  ,;i\.  s  the  deeri  i-e  in  \olmiU'  of  a  cubic  inch  of  the 
HI  III  rid  for  a  ]  ire-- -.me  of  i  pound  ]Hr  sipuire  inch  apjilied  on 
I  ver\  -ide 

C  r=  Modiiln-.  of  Shear  (  )/■.'.  which  is  the  (piotient  of  tor- 

2       Ul    .     i   ' 

-ioual  stre-.s  to  torsional  str.iin 
m       The  ratio  of  loiinilniliiial    conipres-iou  to  lateral  rxtcusion  per 

unit  of  length. 
il  and   ni  an-    measnred    directlc;  the   other  cahics   arc  calculated 

from  till  m 


■#  •• 


KI.ASTIC  CONSTANTS  OK   RoCKS. 


23 


Those  valircs  in  the  case  of  each  rock  are  (jiven  in  the  respective  tables, 
expressed  in  inch  and  pound  units,  and  tlie  results  are  summarized  in 
a  ijeneral  table  on  jiaj^e  6<) 

The  nieasurenienls  wire  made  in  llie-c  units  on  account  nf  the  fact  (jf  the 
teslini;  machine  iniploved  was  jjrailuatid  in  read  pounds 

I'lir  purpn^is  i<i  comparison,  Imwever,  this  latter  table  has  been  recalculated 
in  C  ('.  .S  units,  and  the  results  a/i'  set  forth  in  the  sernud  table  to  be  foiuid 
on  pai;e  <>'). 

In  the  case  of  mel  il.  1'  lisvui's  ratio  is  generally  arrived  at  bv  strelchiut; 
the  l)ar  and  iletermiuiui;  llu-  value  of  tlu  lone;itudinal  extension  dividid  bv 
tlu'l.iliTalconiracliou  Incase,  f  rocks  the  teu^ileslren^'th  beini;  low  and  the 
materials  bein;;  brittle,  it  is  more  couvenient  and  more  accurate  to  make  the 
determination  bv  coinpre-.sin,i;  a  short  bar  or  cohimn,  an<l  determitiin:r  the 
value  of  the  louiiitudinal  compression  divided  bv  the  lateral  e\i)aitsion  This 
,i,'i\'es  the  \alue  desiijuated  as  ))(.  of  which  I'oissoii 's  ratio  is  the  reci])roeal 
Theoreticallv  one  mel  hod  is  a'^  accurate  as  the  other  In  actual  practice  it 
miy;ht  be  siip])oMil  that  the  sliort  compression  cohmins  in  (piotioii  would  not 
evcpand  (piite  so  much  at  the  ends  as  in  the  middle  because  of  tlu'  fric- 
tion a;ainst  the  coinpn-ssion  plates  In  order,  however,  to  cause  these  to  slip 
as  easilvas  i)ossibleo\-er  the  i  ii'l ,  o|'  thecolmnu.  the  ■airj'ace  of  the  rock  in  con- 
tact with  them  was  alwa\s  made  \er\-  >mooth  and  also  was  sli^dillv  oiled  It 
was  fouml  that,  these  precautions  bciui;  observed,  Ihr  expansion  at  the  euils 
of  the  column  was  practicalh-  as  j;reat  as  at  the  center,  where  the  nie.isnre 
menl  was  taken,  tin-  dilTireuees  beiuL;  so  small  that  no  serious  discrepancv 
was  iutro<|uci'd 

In  the  tallies  the  first  traus'.arsi'  line  desiijnalis  the  speci  iieil  emploxad 
as  li,  h,  c,  or  (/  The  second  line  ijives  the  diameter  of  the  specimen,  which 
is  often  sliijhth-  ditTertiit  in  the  two  directions  The  lenjjth  of  the  column 
in  all  cases  was  about  finches,  but  this  is  not  staled  in  the  table,  as  the 
compression  is  not  me<isur<'d  on  the  lot.d  lens,'th  of  the  cohnnn,  but  on 
the  lenijth  of  that  portion  of  it  which  lies  between  the  points  of  attiichment 
of  the  instrmiient 

The  third  line  sives  the  area,  which  is  approximatelv  i  stpiare  itieh  in  the 
case  of  a  scptari'  prism  and  three  apiarters  of  a  sipiare  inch  in  theiaseof  a 
round  cohnnn 

In  tin-  t'our  suceeediu';  hues  the  four  elastic  constants  /•.',  •-.  /',  and  ( ',  are 
j;iven,  as  deliTinined  b\'  each  measuremeni 

Anothci  transvirse  line  contains  the  letters  I'  ir  /',  which  disi.i^nate  the 
two  diameters  of  the  cohmui  when  two  measurements  were  made  on  the 
satne  scpiare  pristn.  these  two  directions  bcini;  alwavs  at  ri,i,dit  angles  to 
one  another  In  the  case  of  round  columns,  on  which  meastnemi'uls were 
freqnentlv  m.ide  in  several  planes,  these  arc  designated  as  "first  holes," 
"second  holes,"  etc. 


A 


24 


AN    INVKSTIOATION    INTd    THE 


l.iiu-h  lubU'  tlu-rr  follows  till-  vaUus  obtained  for  successive  loacliiiRS  of 

,  ,,m.ulsi>i  the  c:.>e  of  eacl.  siH-eiuun.  f.rst  for  coiupress.on    wlun  ll,e 

r,'-M,res  n.ullil.lic.l  hv  four  «ive  nnllionU.s  of  an  inch,  an.lllun  for  lateral 
.■M.  iMsion  uiven  .lireetlv  in  tnillinntl.s  of  an  inch  These  affonl  the  .lata  lor 
eak-nlatin-'the  constants  an,l  for  ..lotting  the  curves  which  accompany  iveiv 

'  In'  the  hRures  for  the  constants  of  iron  an.l  of  one  or  two  of  the  rocks,  which 
arc.  the  result  of  n.easureinents  which  w.r-   made   at    the  iK-.nnms  ol  the 
inv.sti.^ation.  a  sliijht  correction  has  been  „,  ..le,owin«  to  the  tnaccurate  cah 
l.ration  of  the  ,v;tensonuler.  which  will  explain  a  certain  <liscrepancv  winch 
will  appear  if  the  li.nures  are  recalculated 

THE  ELASTIC  CONSTANTS  OF  ROCKS  COMPOSED  OF  A  SINGLE 

MINERAL. 

MARBLES  AND  LIMESTONES 

1)1. \CK  HlCl.dlAN   MAWnl.lC,    lllCl.llUM 

Tliis  rock  is  known  in  trade  In  the  name  of  ■  Helwian  black"  or  "Xoir  fin  •' 
It  is  an  extremelv  fine  ..-rained  black  marble  which  takes  a  verv  lu;;h  poh>l. 
ami  is  used  verv  extensively  in  interior  decoration  U  has  a  splmlerv  Irac 
ture,  breakini;  almo-t  like  ;<lass  ,     •      ■ 

Wlien  thin  sictions  are  examine('  muU  r  tlu'  microscope-  the  rock  is  l.mr-| 
t„  be  so  fine  in  -rain  that  a  lii-h  ix.w.r  is  necessarv  to  resolve  it  It  is 
compose<lol  minute- calcite  umius  in.m  o,,.  mm  to,M„,.Mnm  ni  .liameler 
au.lol  irre-ular  shape,  belweeu  ami  ,„.. mid  which  .ire  o.-casimuil  mmute  1,1ms 
and  s))ots  of  a  black  color 

In  this  verv  fill.-  -r,.iiu-(i  and  even  -romi.lmavs  are  eiul)edded  a  verv  l.w 
l-,r-'er  form-  of  clear  white  calcite,  soiiu-  of  them  ro.llike,  oth.-rs  cireular  m 
sh-me  and  others  po.s,-ssiii.,r  more  conii)lic.iled  outlines  These  are  evidentlv 
ol'or.'anic  ori-iu,  rei,n-s.-nlatin-4  -mall  ira-menls  oi  fossils  I'liev  are  verv 
sparselv  seatteivd  Ihn.u-Ji  tin  rock  rhe  roek  also  contains  occasional 
miniitei,'rainsorcrvsi,ds,.fi-  .11  pv  rites 

|--r,,.,Miients  of  this  n.ck  .lissolve  readilv  in  eld  ilihite  hvdrochloric  acid, 
■  rivm  ."..IT  a  fetid  o.l.ir  and  U-aviii-  a  cusiderable  am.nint  of  a  li«ht  lloeculent 
r.si.hu-,  black  in  clor  an.l  ;,i,].arei,llv  ciisistiu-.^  ..f  s.mie  form  of  bitumiiions 
„l;,,l,-r       In  the  i-esidue  llu-n-  are-  also  a  l.w  miiuile  strains  ..f  pvrite 

Plate  1  A  is  a  clor  pr.,e-e-ss  ph..t..i;iai.li  ..I  a  p..lislu-.l  siirlaee  ..f  this  marble 
and  Plate  I  li  is  a  phot.,imer..,;;iaph  of  .i  Ihin  se-eli.ai  .a'  llv-  rock,  taken  in 
..rdiiiarv  li'.dit  and  ma..'iiifii-<l  -^7  diameurs 

\  s(|iiare  prism  ..f  llu-  n-.k  of  the  usual  elinieiisions  wasempl..ve(l  to  meas- 
nre  the  elastic  cnstants,  and  the  results  are  set  forth  in  the  table  f..iiiid 
on  paire  25 


BLAr^K    BfLjiAN    MARB'.t,    ("nOIR    FiN"). 


KLASTIC   CONSTANTS   OF    ROCKS. 


»5 


Hhck  Hilniiin  \farhie. 


Sl/t* .  . 
An  I 


n 

c 


I-ii.iil  I  tn  |Hitiii<l>i 


I,(Kh> 

),(X)0 

■,(KK> 

>,fKX>  . 

\(NK> 

•,(J<K) 

t,(KJ<) 

(,CKKJ 
!,<>fX>  , 

.CKM) 


.  Wi  X  ,9(i 

.96 

■<22 

1  I.OVIMHM) 

.278 

8..KI.I.IIIXI 

4,.V1().(MH» 

I.<inL'ituillll:il 
0'iii|>ri-^--iini 

uniiltiplv 
ri-inliiii;>   liv  -1 
for  tinlli'>ntl)>l. 

I  .■l.T.ll 

t  Nt«  n^iiiii 
Miiilli.iiith-j. 

o 

O 

^4 
,SI 

-(> 

1 1(1 

KM 

147 

..'., 

.-40 

i\  I 

I  no 

14.S 

lis 

.S,S 
hi 
.1° 


.'DC  J 
l>i 

I.S7 
■  ,u 
104 

7,s 
,S1 

4 


Tlic  elastic  consttiiits  were  fmind  to  be  ;is  follows: 

£■  =  ii).o7u,(xM);         1  '  o  2-i>\         I)      S,.v  1,1.000 :  C-4,?^o,o<)o 


9000 


dSOOO 


Xy 

V^ 

.^ 

f 

^ 

y 

V^ 

X 

/^ 

0             4 

C           8 

0            li 

'(?         16 

0           21 

10 

I'll 


S  TRA  IN 
('}.-    lilack  Hi-l^ia:!  MarliU',      Stri-ss-slriiin  curvi'S. 


A  plot  of  till'  reiulinss  is  jjivi-ii  in  fiijuri'  6,  from  which  it  is  clcarlv  seen  that 
the  rock  is  practically  free  from  hysteresis,  and  that  within  the  range  of  pres- 
sures emplove'l  its  elasticity  is  almost  perfei!  !  represetil';  longitjj.-Una! 
compression  and  II  lateral  extension. 


26 


AN    INVI'STK;  \TTc>\    INTil    THK 


wiini:  \i\Kiii.i:,  i'\wi<\u\,  it\i,v 

A  \v!iik>,  v.rv  liii.-  ■;imii!.i1  suvliin.iil.il  mirlili'  lliiiU-r  llir  iiiirmsi'Dpi'  il 
isMtn  toi()iHi>i"i';i  tiio-,:iU-,,tc:iUitii;r;iiii^  In  this  iii(.s;iic  wmif  uruiiis  :.ri> 
liirucr  lli;iii  .itluTs.  ImiI  llur.-  i-  no  in.il  .lilT.  nil.  .•  in  tluir  r.l;itivf  si/is  iitid 
llu-  ivir.ii;!'  ;i:iin  n|-  ili.  ro.k  is  iiiiilorin  tlir..ii.;li"nl  Tlif  ;iv«r;ii;f  di^nnctir 
nf  i-.,Uiu".rvslaK  clnMls  i]ii)r>\imal.s,,  _■  iiiiii  •nuM;niins.>>iiir  a^iiinsl  mic 
.iiintli.  r  aloii-  sliarp  and  nsuallv  s(iai.;lil  lin.  -,  Tin  re  is  no  tracf  of  I'olialion 
in  111.-  rock,  nor  i-  tlur.'  anv  traiv  ..f  llallmini;  <ir  clotiiialion  of  llio  ','rains 
ill  aiu  on.  dircclioM  l"!u'  roik  ifi  iK-n.-.-Uv  inassivf  Hrlwriii  crossfd 
iiii-ils  ill,-  i-ilrih-  in  lividii  lis  c^lin-iiisli  iiniforin1\  and  sliow  no  sj^r,,^  ,,f 
l)ri->urr       S  lUK- of  lln-iii  >li  nv  a  fi-u-  Iwili  laiiulla- 

A  oilor  |)ro.-.-s-,  |)li.ilo-|-.i|)li  ..I  a  polisli.d  siiriai-i-  of  llic  rock  (1111)1.01.1 
is  ^liowii  in  I'litr  II  \  and  a  plw  .i.nnioro-rapli  of  a  lliiii  vrtimi  ,,f  llu-  roi-k, 
lakni  in  ..rdnnr\   li^lil  and  iiia;nilird   -■:  dianuUrs.  is  sli,.uii    in  Hale-  II  :> 

Tlir.-i-  ^iHTini.-ns  ,,f  lIu-  rork  wm    ii->d  in  uiiasurinii  llu-  (-laslir  toilslaiils, 
lv>n  s,;n.ir'-  iirisMi,  i.i  and  !■)  and  a  roiiiKl  odiiuin  U  )      Tw..  s.ls  ..f  iiuasiin- 
iiuiils'vvnv  mad.   on  h^ih  /.  A\h]  r.  ili.-  iiislnnn.nt  lu-iii-  as  usual  alllx.-.l  to 
111,   spc-,iin.-iiinU\o  p  i-ilioii^  al  rl-lil  aiij.-s  l.,,,ii,-  aiiot  lu-r  iil.-a.li  ■p.-.-iin.n 
!n  lliis  wav  liv.-  .-oiirilrt,-  s.is  ..f  ni.  asur.inn:!-,  w.-r.-  inadt-      Tlu-  r.-.nlls  an- 
s.t  fnrlh  in  111.   1  ilili-  on  pa-;;i  .•;. 

Ttu-  imaii-  of  111.-  n  Mills  ..l.l  lin.-.l  for  tin- r.-spr,-tivi- ilastic  i-oiislaiits  an- 
as   f.  ilI.lWs. 

/•:    -  S,.,((.  o.io;  T    -u   -744;  /'       5,.l4'i.<io'>:  '  -i.lsf.ooo 

■ni.-.lilTircii.->-l).-tiv,-.n  llu-liii;lu-st  andl.iu.-sl  d.U-rinin  ilioi|s..f /Ms  4.'.)..  .00 
pounds 


^ .^ 


la... 


I,  ;irr,ii  1 111.11 1'U", 


5  FRAlIM 

ti'iiij.ii'J  S;u>^  ^iTiiiii i-ur\t-s 
I'i-^iiri-  7  shows  till-  n-snlls  .,l)laiiu-.l  fr.iin  >pi-..iiiu-ii  .(  in  -^'raphic  form. 
I  upn-sonts  lonnitu.linal  onnprc-ssion  ami  II  Uit.nil  .-xU-iisi..n  Tin-  Ins- 
U-rcsis  is-r.al.r  than  in  lli.-  cas.- of  lUl--;i-ni  Ma.  k  ..r  I',  nm-ssi-v  iiiarbU-,  Init 
is  abont  llu-  sanu-  m  ani.iuiii  as  liiai  sl„.un  i;>  l'...  Wrmont  murbk-  and 
tin-  Tri'iUon  linicslom-  fniin  Montrt-al 


>*f*:^^ 


*.      PMOIOOWAPM   Of^    P(.ii  ISMFO    "i.  «F*CF,   (NATLHAI.   S'ZE' 


i   • 


d 


%,itf,ii*. 


RI.ASTIC    CONSTANTS   i>F    ROtKS 


'7 


No. 

Arc.i 
I- 


n 

I  (iij     I  "> 

I    f)7 

s  I  >n 1 


b  b 


I    IIU 


■H   M 

A  IMIO 

H    J  1 1 1  Ml  H  I 

H, 

IIS.IHK) 

»7  * 

.•■•^ 

^.,'1 

s  •'.' 

)  114  in 

*..  IIHI  (HHI 

>. 

'•iit,lHHl 

\.\ 

.11   IK  HI 

*   .JIltl'tHI 

V 

1  ;n  iHKi 

f..M.mi'iN\i   L<'*ii'ki  >jii-.N       MrLiillv    kKAl'iN'i'^  nv    4    iok    MiiM'iNini. 


fo.i.l      III 

Si  lit' 

,..UII,I~ 

r. 

I.OtKI 

o 

?.»"H> 

15 

(.!""' 

:s 

1.1  I"' 

I  rn 

<i,.  >  K  . 

1  IS 

(l.lXXl 

1  ^o 

7,(MM( 

-■Ml 

?(,(MK> 

li.Otxl 

S,(  M  M  I 

7.(  N  M  1 

.M'l 

6.()<Hi 

I>S 

5,1  N  H  1 

I  S-' 

4.1 1 » 1 

1  l> 

(,<«H1 

.^.' 

.'.(KH) 

44 

I  ,(XX> 

(1 

Slilf 


irri> 
-'I'l 


1 7' 


4,s 


.'(Kl 
-MS 


irui 

II  IS 

S( 


II  Kl 

1  SS 

.'f>S 

.'S^ 

I.AII.k  VI.    l^XII.SMCN  Mri  LlltSlHS 


N... 

II 

6 

fc 

c 

Si/i .    -  . 

1    lUi 

1    016 

1    IIU 

98S 

1 

Sulf 

Siilf 

!         LuLid    in  ix.tituNt. 

/'. 

U. 

1,1  X  Ml 

() 

0 

1) 

0 

1" 

IS 

17 

4S 

),(MMI 

(>2 

T.S 

;.« 

•aS 

.     4.1"  X' 

I'.S 

1  10 

1(1^ 

1  i<> 

S.lHHl 

I, ill 

14s 

14' 

'7S 

O.ixxi 

T'lS 

I".! 

177 

217 

7,(XH)      . 

.'IH> 

S/KHt 

II    1  II  M  > 

.... 

170 

.... 

....        ^ 
177        i 

,K  (  N  H  1 

fl.lXXI 

J'7 

5,(XK).  . 

'54 

i           IS" 

Iho 

iNc 

4.(K«l 

ms 

l.'O 

1  1.' 

i.V 

(.(««! 

70 

,s  ^ 

75 

11:0 

2.""" 

IS 

40 

IS 

,S  ) 

j      i,acx>.  ■ 

,V 

*             1 

'              i 

4 

i 


28 


AN    INVI'STlGATKiN    INTl)    Tlli; 


wiiiTi:  m\i;i;m:.  \i:;jMii\r,  r\iTi:ii  stati:> 

riiis  is  .1  pmv  uliilc  iiMihU'  iiiili-,liii^iii-!i,il)li  I'r.im  tin-  CiriMra  iii:irl)I( 
ill  :i  li.iiiil  >|HciiiU'ii  I'lulir  tile  iiiicri>>i'n|H'  iKo  \i  n-.r'iil)Ks  lliis  ruck  \<r\ 
closely  Till' ,:,T.iiiis  she  i\v.  Imwi-vct,  a  smiikwIiii  -rcairr  \  ari.iti.m  in  nlalivi' 
size  and  lluii'  is  a  UikKihs  !■■  a  ll.ii  ii  nin;,.  in  ,,in  diinlinn,  i;i\in.!,'a 
viTv  faint  li.lialMn  i,,  the  r..,-!  i  in  tin-  a<-c-..nnl  mhIv  a  sin,-li-  s|K(.inHii 
was  iisid.  siiKT  the  I'nliati.ai  in  ipu  Mmn,  alllmuiji  harih  pirit|ilililc,  nii;,'lit 
alTi'ft  the  ilasticitx-  cf  mik,  anil  it  uas  llurt|'i>rc  ivnisidi nil  sal'tr  to 
rilv  iiiion  tlu'  Carrara  niaiiil.'  in  nuasuiiiii,'  tin-  I'lastii-  i-oiislanls  of  this 
class  of  rocks.  In  the  |ii:sni  of  WrnioiU  niarlilc  cniplox  cil.  the  I'oliation  lav 
ill  llic  ilircclion  of  tin  lon-cr  axis  of  tlic  ])risni  It  is  prol.aldc  that  this  folia 
tion  uonlil  not  be  lonml  in  all  Wrinoiit  niarlilcs.  but  happcniil  to  be  [ircscnt 
in  the  specimen  procured  I'or  exaniinalion 

.\ph<itoniicroi;rapliiif  alliinsectionof  the  rock,  in  this  case  taken  between 
crossed  iiicols  am!  iiiaijnitieil  u  diameters,  is  shown  in  Plate  III  A  color- 
process  plioloijiaiili  wis  not  prepared,  since  the  rock  in  such  a  photograph 
would  be  identical  in  appearance  willi  the  Carrara  marble,  of  which  such  a 
photot;rapli  has  alreaiK   beet)  ,i;i\<ii 


1  ,1111. :,ii    \!,i,N,. 


1  cu;      I  1112 


\.iy,d  (ill  ixmiiiis' 


7.,S't 

,n:ii 

t 

:<>.s 

S   Ul.oi 

1 

1  KiiKitiKliii.il 

fniiiiirt^'-iMn, 

'  iiitiltiph 
icuinii.!-  I.\   4 
for  inilliiiiithsi 

I.itfr.il 

\Il  llsHUl 

lltUoUttls 

() 

o 

4" 

I  JO 

KK) 

■57 

l,vS 

J<X3 

'7  ' 

1'"; 

1    (O 

i-',i 

IDS 

1)1) 

7.S 

SI 

,V) 

5 

1 

iiitt 


w^mmm^msammmm 


M  :. 


H       5> 


i^M 


.EhMCN'     V',HBLt. 
PHOTCV  CROii'ilfM   wt    Iii'i   SH.T  o->.   '■>  31    D'iV-M'. 'J   S  r^-.^stC'^ 


I 


I  I 


I  rf-»\>^»^  Ti'-'^ir 


mS 


ni.ASTIC    CONSTANTS   OF    ROCKS. 


29 


I 

{ 


A  s(|ii:iri'  prism  iif  tlir  in;irhU'  was  i-mpli.vvil  in  iiuasiiniii;llipil;i  .tic  i-on- 
slaiils,  aii'l  i!h-  (k'Uiilc  I  ri'^ulls  ari'  <j,\wn  in  tlic  :iccii;iipaii\  in.;  lalili',  and  arc 
ri'pri'siMitfd  in  jjrapliii'  I'niiii  in  litinn-  ,S  I  rcpriMnt^  Icn^iludinal  t(iin|)ri-s- 
sion  and  II  lalfral  ixlinsicpn. 

'I'ln'  riillnuin;;  art'  ihi'  \aliii^  <il)taint'il : 


/; 


>') 

j.oou : 

7000 

ZlSOOO 

0  1000 

I)  2h\: 


II 


3,  y-\  I  .txyn 


C 


I'M.  S.      \\.iinitiil  liiiilik'.      Si  rfss-sir;iiii  I 


M  \niii.i:.  ti;\m;ssi:i;,  r\iii;i>  static. 

This  i-.  a  niarhlc  kn'iun  in  tradi-  as  "I'ink  Ti'nni.sMc, "  and  is  Iarj;.h- 
nst-d  I'lir  (k-oiiralivi-  unrk  II  lias  a  hmwnisli  pini<  coicr  and  wlii-n  polislu-d 
shows  a  sDnu'whal  niollk-d  siirfaco. 

I'ndtr  llu-  microscope  it  is  seen  to  consist  of  rather  lari,'e  irrcjjniar  shaped 
and  often  disliiiell\' roim<k'(l  individuals  of  c:ilcite,  which  arc  fitted  closelv 
toi;ethcr  alons;  sharp  an<l  in  some  cases  creiinl  iu'd  lines  Tliese  indi\idnals 
are  almost  invariahlv  traverse<I   1)\  row  laniellx.  dne  to  polvsvnthetic 

twinniiit:.  and  are  oeeasionallv  twis  o  that  tliev  show  an  iiiiilnlator\  ex- 

tinction Hetween  these  larije  calcite  .  di\i<lnals  there  are  freipienlh  present 
masses  of  what  is  apparenllv  a  l.il)nlale  coral,  showiiii;  she.ives  of  tnbcs  which 
in  cross  section  are  ai)i)ro\iniateIy  circular  in  onlliiu  'I'lie  c.tkiti-  indi\id- 
tials  are  often  embediled  in  this  coralline  maierial.  as  if  thev  had  '.een 
d'.'velopeil  hvits  recrvsl  illi/atiou ;  in  other  c.ises.  however,  their  ajjpearanec 
sn,<,".;ests  a  derivation  from  crinoid.d  frai;inenls  .Vl!  the  tuhcs  of  the  coral,  as 
well  as  the  interspaces  of  the  liihes.  if  an\'  existed,  arc  now  I'llled  with  calcite, 
so  that  the  substance  of  the  rock  is  conlinnons,  resnltiii),'  in  a  compact  marhle, 
I'ra'.,'nietitsof  the  roek  dissolve  readih-  in  cold  dilnte  hvdrochloric  acid,  leaving 
onlva  verv  Irillin;.;  risiiliie.  which  has  the  color  of  the  rock  itself 

.\  I'ol.ir  [irocess  photoijraph  of  a  polished  snrfacc  of  the  rock  is  shown  in 
I'laU'  I\'.\.  and  a  photomicro!,'rai)liof  a  thin  section  of  the  rock,  taken  in  ordi- 
n.irv  li^dil  and  maijnified  ,'7  diainelers.  is  shown  in  Plate  IV  I).  In  this 
photomicroirraph  a  fra,icinenl  of  the  coralline  maierial  is  seen  in  the  center 
of   the  field,  while  the  border  is  formed  chielly  of  individual  calcite  grains. 


■Itiipli 


,V) 


AN  i\vi>Ti('..\TiiiN  INTO  Tin; 

I.  nil U.'»W., 


St., .  ,  - ,  II 

M,.,.     i  I II  i;      ■'■I 

\ri.i  I    "" 

/,  •),lli.,n,i, 


1  .«.!  Ml 


/. 


S.TTn.ODI 


l,slo,u(ii>  ,i.S7i.i"«l 


l,.l  lO.IB" 


,.s,;ini.iNM    i..MrKi-i"N      Mil  mil    Kiamm.-  "\   4   fn   Mii.i-l.'Nriii.. 


r 


1 1 


i.M.i   111 

1  ,n.  M  1 
1     J,i«»> 

o 

2ii 

1          ^,<  M  H  1 

'>S 

i    ).(.<"' 

1(KI 

i    ^,.hh. 

T   V» 

1       (.,(M  !■  • 

I'lS 

^•l.k■ 
r. 


7  S 
t  ii> 
I  ^i> 


I  in 


Si.k 
I 


1  1^ 
I  M 


I --I 
I  ,(1 
1  1" 


1  lO 
!0 


IMIKAI,    ^;\ll.^^l■r^    -    Mllll^MII- 

„  /,  I, 

'I'll,  'Ml  I    "" 


Si.l.- 


SicU- 


l.,,.„l  ,.1  p.  1111.1- 


I 


Mill 

/■ 


t.l»"l 

|,0(K'- 


-15 


1   |1 


>         I 

)    1    ,\ 

.1  tll.U'Kl 
.S40,I)IK) 

h. 

Sidt 
P. 

170 
Jit) 

2')0 


I' 


«i  «M'.  PL4TE   IV 


.  I 

1 


B,      ^f,,jloM^r:«oaH«FM  OF  thin  SECriON.  (X   27  Di«M,- OBDINiR-T   liOHIi 
MABBIF,    Tfr.riES'.Et,  ("pink    TENNHSSfc'E"!. 


J 


I. 


■-r.  ..,'j*r 


.*.'^'''<S%»'^"^'- 


I 


ICI.ASTIC    CONSTANTS    OF    ROCKS 


^1 


Three  square  prisms  of  the  rock  were  employed  in  measurinj^  the  elastic 
constants,  and  on  thesi'  seven  sets  of  nieasnrenietits  (jI  vertical  compression 
and  six  of  lateral  extension  were  made,  as  shown  in  the  tahle  on  paj;e  ,50. 

The  avera','es  of  the  reslllt^  obtained  are  as  follows: 


/•; 


i),(M)6,o(Mi; 


;5i,^; 


I)    -  5  <)67,oiHi; 


^, 607, (XX) 


The  dilTerence  betweiii  the  highest  and  lowest  values  obtained  for  I)  is 
,36o,(xm  As  will  be  seen  by  consulting  fijjnre  i)  the  rock  is  almost  free  from 
hysteresis  In  this  l]f,'ure  1  represents  the  longitudinal  compression  and  II 
lateral  extension. 


I 


0  40  SO  ISO  160         100         e40        ZBO 

STRAIN 

Kic.  9. — 'IViint'ssee  Marble.      Stress-strain  ciir\es. 


FOSSII.IFICROl'S      l.IMKSTilNIC       (TRICNToN      FllKMATIUN),     MILE     END      (JlAKRY, 
MoNTRIvAI,,    CA\\l).\ 

This  is  a  typical  fossiliferous  lilne^lon^'  of  the  Trenton  formation  (Ordo- 
vician).  It  was  taken  from  a  massive  bed  j  feel  in  thickness  known  as  the 
"F.ower  Bed'  at  the  <|uarry  from  which  the  gnater  part  of  the  building  stone 
for  the  citv  of  .Montreal  is  obt.iined  The  rock  is  dark  gra\-  in  color,  and  is 
compact  and  solid  in  character 

Under  the  microscope  it  is  seen  to  be  composed  of  fragments  of  fossils 
which  are  in  some  cases  angukir  and  in  others  more  or  less  roiiudeil  Thev 
are  chiellv  bits  of  Monticulipora  and  of  Crinoids  and  show  the  structure 
of  these  organisms  perfectly  These  fragments  lie  embedded  in  clear  transpar- 
ent calcite,  occurring  as  large  individuals  which  form  a  continuous  mosaic, 
giving  rise  in  this  way  to  a  perfectly  compact  rock 

A  color  process  photograph  of  a  poli-.ied  surface  of  this  rock  is  given  in 
Plate  V  A     A  photomicrograph  of  a  thin  section  of  the  rock,  taken  in  ordinary 


m 


,<2 


AM    IWKSTIC.ATIdX    IVTO    TlirC 


li;,'lit  Mini  iii:i>^'iiitu'<l  ."7  iliaiiulir--,  is  sliinvn  in  I'liite  V  li  In  the  phntomicro- 
,i,'nii)h  a  l'r;ii;MKiil  ni  ;i  MnMlii  iiliporid  is  sicii  in  tlif  ivtitiT  iif  tlif  field,  wliilc 
tlir  ihirktTarcMS  about  tin.- jxriplKTV  nl'  Ihr  field  art'  Crinnid  iiginents,  each 
with  a  seeiindary  en!arj;etiient,  ennsistinx'  i>|"  pure  caUite,  siirt  lundiiifj;  it. 


I'rtii'.i'i   I.tmt^ti'Hf,  Montual,  Canada. 


N.. 

Size. 

.\rc:i 


'184 


I, 

9K4 


u 
c 


'J.JM(l.fHK)      <J,49(>.nt»0   I  y,I»0,tMM)       8,9JU.(HM) 

(I, ISO. (KM)       h  4.Sll.(MHt 
.(.7II»,(HM1       l,77,S,uim 


2,«5  j  .2482  I 
(..I'>n.(MH»  I  .S.820.(HM)  ' 
,t,f>4'i.<MK)    I   .t.4I5.(«K)   I 


i  I.alerul 

Lnn^itudtliui  ctiiiiprcssion.  -Multiply  rciulinKs  by  4  for  millionths.  i      fxti-n^i«>n 

(inilhiinthH). 


I.iiuil  I  in  piiutul 


I.OOO. 

^,ooo. 
J.ooo 
4,cx». 
5,ooo 
6,ooo 
7,ooo 
8,ooo. 

Q.OOO. 

S.ooo. 
7,ixx). 
f>,aoo. 
5,ooo. 
4,ooo. 
3,ooo. 

2,000 
I.OOO 


Side 
V. 


,SO 
f(0 

I  to 

ISO 


SiJe 


o 

i|0 

'7.S 

J  JO 


Side 

t'. 


ISO 


Suit 


i)o 
'  .\" 
170 
-,io 


,U 


<).S 

MK* 

I.VS 

140 

■T.'i 

ISO 

:,;: 

I  So 

-^ 

f  "-o 

I  111' 

i^.S 

i.pi 

147 

I'l 

1  1,5 

I  1" 

l)o 

IOf> 

106 

'I.S 

'1,5 

18)   j 

ys 

'■5 

7.5 

.'SS 

54 

54   ! 

55 

3-' 

35 

0 

4 

5 

J 

.1 

BO  120  16(1  ZOO  140 

S  TRAIN 

Kiu.  10,  — Tri'iitoii  linicstoiie.    Stress-slrain  curves. 


TOMiCROGRAPH    OF    Th'N    SfCfrON,    U    ^  .'    UAM- OH  JINAM 
TRENTON    LIME'^TONE.    VONThtAl,    CANADA. 


^tm 


I'l   \TK-    CciNsT.WT 


Tile  .li.li.-  r..,i-.t.,nls  ,,r  i|„-  „„k  u.Ti-  iii.isi,r..l  ..ti  Iwc  rnmiil  (■(.Itiiiiiis, 
fniir  iiUNisMH  111,  ni  ,  Ml  V,  tti.-  ilo.riipr.  -,si,,„  ,,,i,|  ,«,.  n|  l,,|,ril  ,  At.iisi,,n  1„  i,i^^ 

IIIIHIC  'lllC  n-Mllls  ;in     ,;l\(  11    Ml    tllr   l.lhlr    im    [);i;;,.     ;j 

Tlw  MSiri-.-,  .if  ihr  h  ,iill ,  oIiIiJihmI  ,in  ,i^  loll.uvs: 


>l.  _'i  >>.i  »  M ) ; 


/'       *i.i»>-,>( 


!.fHf),{)(>n, 


^  Thi^  cliiririm-.'  IhIu.cii  iIic  lii-lusi   mi.l   luw.st  ri;i<liii-s  for  />  is  Wk,,,hk 
The  .vsiiits  n|-  il„.  Mi.iMiniii.iil  ,,i  s,Hriim'ii  ,i  :irf  >li.iuii  In  -nipliic  form 
liKtirc  lo      I  iipri^iiii-,  l..ii-iui,liii,,l  o.mprisN|,,ii  ;,ii.l  II  lali  r;il  ixl.nsi.ni 


Ml't 

in 


THE  KLASTIC  COWSTANTS  OK   KOCKS  COMPOdliD  OF    MOKE  THAN 

ONh;   MINERAL. 


AC.D  PLUTONIC   KOCKS 


i.K  Win;,   iiA\i:\M.  n\i,v 


riii.u.ll  kiMuii  -ruiil.-  i^  pile  pink  III  color,  aii.I  iilHioii-li  oiarsrr  in  )>niin 
111  111  tlu'  rocks  iiisi  iliMTilM'!.  is  M  -r.iiiilc  .,f  nuiiiiiin  -r.iiii  ;iii.|  is  v.rv  iiiiilonn 
in  cli:ir,u-i,r  It  rcscinhU  s  ih.-  I.ilv  l.ukr  -r.niilc  closclv  in  appcanincc, 
:illlioii',;li  it  is  a  little  (iiur  in  i;raiii 

It  is  coiiipos.-.!  cssciitiallv  of  ipiarlz  an. I  ..rtliod.is,-.  uitli  vcrv  siaall  pro- 
portion of  liioiiic:  ilH.  hiotii,.  i,  in  places  sonuuli.it  allcrcl  todiloritc,  and 
llu-  orthoclascis  in  places  soiir.wIi.u  turbid  from  tlu-  presence  of  kaolin,  Inil 
the  rock  may  nevecllieless  hi'  cliaracteri/e<l  as  a  viT\  fri'sli  one 

It  Ins  a  l\|)ical  hvpidioinorpliic  sTaiiiilarstrncliire  The  ortlio.-lase  often 
sliows  faint  micropertliilic  inlcr-rou  tlis,  .md  s.mi.-  plai;ioclase  is  pres,  ni  as 
an  accessorv  coiislilniiU  The  (piarl/  iisiiajlv  sl|,,«sa  verv  fa.nl  nndnlatory 
exlinciioii,  .dllioii^rli  il,;,  j,  j,,  ^,,,1,^.  e;ises  cpiile  distinct 

A  color  process  pli,,lo;^ra|ih  of  a  polished  siirl'ace  ..f  the  rock  is  shown  in 
I'iatc  \-I  A,  and  a  plintoniicro-,aph  of  a  thin  section  of  the  rock  is  sIk.wii  in 
IMate  \'I  :i  The  latter  ua  taken  Ijetuceii  crossed  nicols  in  polari/ed  li);lit 
and  is  majjnified  ;(.  diamiters  The  crack  seen  crossin.i;  the  rock  in  the 
|)liotomicro,-raiili  was  ilexeloped  diirin-  the  i^riiidini;  of  the  thin  sectr.n 
and  does  not  in.licaU  anv  shatterin-  or  lack  of  continnilv  in  the  substance 
of  the  rock  itself 

Four  ronnd  columns,  h.  ,-. ./  and  •,  were  employed  in  tlie  mcasnrenu-nt  of  the 
elastic  constants  of  this  -ninite  On  specimen  /.  a  double  set  ..f  measure- 
ments was  made  in  each  of  the  planes  f  and  /'.  which  planes  were  at  ri-ht 
an-les  to  one  auotlicr  In  tin-  case  of  column  c  two  sets  of  measurements  were 
made  in  Uvo  planes,  also  at  ri,i,dit  angles  to  one  another  (r-ferred  to  us  "first 


M 


AN    I WICSTIOATIDN    |M,i    THtv 


Ih.U-.     .111.1       M.nM.I    hnl.s      i         I II  ■  n|,„„„  ,/  f,  ,„r  s.  1^  ■  .f   l„  .|.  s  VN  .  T.' llrill,  .1    s.,-,s 

'"'•"■'■' 1111  isiinnuMK  ,,„  |,„„  ,|,.„i,.lr,,l   ,.l,,n.s.   iiukiin;  ..iikUs  ..f  ,," 

"111.  ...uanMilur  Tlu-  li.st  s,  ,  „n„,l,  ..  |,„„,,,,r,  „,r,,|..,.vtiv. .  v,  m.Msurr 
111.  Ills  u,  r.  „u,lr  M„  111,  MoMhl.  tliir,!.  ;,m,I  i,,„rlli  m  ts  n„K  ( ,„  ,,.|„imi.  ,  a 
miil;I.  Ml  ,,|  iiir.iMiniiu  UN  u,,s  ...mi|.I.  I.d  ulun  Hi,  i,.|uiiiii  t.n.kr 

In  lliis  vv,,\  l.ii  iiu.iMiniiirMl.wf  wrlKMl.nii,,,r.ssi.,ii,,ihl  six  ,,f  l„t..ral  ,x 
liMM.iii  uirf  ..t.i.iim.l      Tlu    r.Mills  ,,i.  pr.Miii.d  in  il,,.  i,,l,K   m,  ,,;,^;,.   ,, 

I  111'  .ivcraKiN  "i  ilir  risiills  (ilil.iimd  an-  as  i.pHous: 


/■:    fi.N  5  i,, 


"      ".-VS;         /'      4,6.q,,,«,,       (■       .•.,7,4,,s,„. 


Tlu'  (lilT.r.-mr  Ik.(«,,ii    tlir    liij-lust  and  l.nv.si   .,  Mills  cbtaiiiMJ   U<t  I) 
ainoiitits  til  siKi.iHHi 


'sTBAf!^       ^^       ^°       ^^       *"*'       ■•'"' 


BO  lio  160 

I'l'.    M.      H.ivin.,  Craniu-      •<triw  strain  ciir\.-s 


_  As  nunun,,..,!  ,„  ,|„.  ,.|„,,|,r  m,  il,,.     Appliralioi,  ,„  ,1k-  Mul, ^i,,,,,,,. 

e.m.pr.ssi„i.  i„  th.-Cas.  ,„  l<„cks,  ■  in  „r,krt.,  nh.aii,  cnsistiiu  ami  r.Iial.U 
results,  i|,c.  speni.ui,  ,,1  ,1,..  rn.K  and  Inr  thai  matKr  llie  sam,.  is  true  n|  ,1,.. 
MKciuui,  ,„  .,i,v  iiu.al  il-  „,  las.ic  o,ns,a,ils  arc  ,„  In-  dcUminud  nius, 
lirst  h.  1„,„.1„  ,„  •■„;„,.  „|  .,.s.-  h^  l„a,|,i,K  ami  nnlnadin-.,'  it  several  tin,.  - 
111  Mien^ss,,,,,,  einplnvinj;  eaeli  time  a  pressure  eijual  ,n  the  niaxiinun,  l,,ad  to 
whieh  the  spie.nien  is  to  he  s„l,j,,.,,,l.  .vlun  H-.  i.ieasureiiients  are  siil.se- 
i|iientlv  made 

Asa  matter  o,  i„„.res,  ,„  ,!„■  eas.  of  the  Havem.«ranite  (as  well  as  i„  ihat 
"1  ti.e.sianstead  granite  referred  to  later),  nadin,.swere  taken  durin,  ,!,.■  lirst 
loureveles  m  compression,  wluii  this  state  of  ^.^se  was  Ix-iin;  imin.eil,  ami 
tile  results  are  jmsented  ,i;raphieally  in  lij;ure  \2. 


■m 


Hi 


i 


ELASTIC  CONSTANTS  OP   Ri  CKS. 


35 


Granite.  Haietui,  Italy. 


Va. 


Size. .  ,  978 

Area..         .75 
Side. .  .  v. 

H 6,620,000 

» 2483 

0 4,J8n,oao 

c 2,6so,aoo 


c 

.978 

75 
1st  hole- 


I        .978 

I.    :"_„ 

'     2d  hoirs 


Sd  holes 


6,7.*U,1)00       7,4.l(),lH« 
.2525  24(.S 


f..«J,Sl),mM)       0,<M(I.IMH»       (».84t>,IM«)    ,   6,H40.(M>O   j   6,62(>,l>00 


€ 
.978 


.75 


^47 


2hS 


2SltS  2V»,S 

4..SJ0.1MM)       4,HH0,tKMt       4.M.S,(MM)       4, M.S. 000       4.470,(HHi       4.H.SO.0(H) 
2,6H2,(100       2.9Ht).tHHi        2,780,(MM)        2,7«O.IMM»        J,7iO,000        2,700,IKW 


4th  holes 

6.730,000  I  6,620.000 
261  2495 

4.540.000    i   4.680,000       4,420,000 
2,63l,OIK)       2,670,000  |   2,645,000 


257 


Load  (in 
I  pounds). 

I      I.OOO    i 
I     2,0(X)    ! 

i    3,0(xj 
i    4,ooo   ! 
i    5,ooo  ; 

I     6,(KX>    , 
7,f>fK) 

H,CXM} 
(),<KK) 
S,(K>0     I 
7,(KH.( 
f»,(KK.) 

4,0(K>     I 

^,rKyc^  j 
:;,ooo  I 

I.OOO    ! 


No  . . , 
Size  . . 

Areii,. . 

Side. .  . 


I.OOO 

-\ooo 
3,ooo 
4,(X)(). 
5,0(X> 

O.tHlO 

7,ootj. 
S.ooo . 
0,000 
8,<xxi. 
7,ooo 
ft.ooo. 
,5, (WO 
4,ooo 

2,UUU .  . 
I.OOO. 


I-(>Nt;iri!lilNAL    LOMI'KLSSia.S     -MlM.TIl'LY     Kli.\l>IN<iS    HY    4    FOR     M ILLIMNTHS. 


.it  5 


.^'5 


6f> 

,i 


« 

() 

f><) 

7" 

ll.>- 

i.V> 

'7.i 

I  So 

-\V> 

J.ll) 

J  NO 

VKI 

.iVi 

.!4-' 

(.Sil 

400 

4ln 

tv> 

(■"-.S 

410 

Vli 

,((|u 

-■'*.^ 

U-' 

-V!i 

-'.i4 

I  7(1 

J114 

I  JO 

1 1.^; 

,?"5 


,!",i 


I.A1I:KAL    lixri:NSH)N  — MlLLIliMHS, 

.f7X 


2,15 


0 

0 

0 

0 

80 
■45 

.60 

.¥>=. 

.■il.S 

,<'o 

l(i,S 
4i') 
4''5 
420 

,?o.i 


.!"5 


^45 


245 


2.*5 


2,!5 


978 


25.? 


225 
ityo 
<IO 


f 
.978 


24'' 


246 


.^6 


AN    lNVi:sTir,  \Tlii\    TNTi)   Tin: 


The  curws  rcpri-cnt  the  ri;i(liii,'sf.>rlnnt;ilii(IinaU-oiiii)r(>si(in.  and,  aswlll 
Ik-  seen,  al'ur  the  Im^i  cvile  nl  o.iui.ri-.-i..n  the  roek  .lid  not  return  .inite  to  its 
original  position,  hut  thi-  iniperleetiou  in  ela-^tieitv  beeonies  proijressively 
smaller  ill  the  sul)sei|iienl  loadin-^  till  ill  tlie  fourth  eomi)re-.si.in  evele  the 
return  is  ahnii-.t  perUet  and  the  !i\>leresis  ver\ Mnall 

l'i,Mire  I  1  shows  tlie  eiirve-  obtained  l)v  i.lotlin-  the  values  seeured  from 
the  measiirenunl  of  the  .lasli.-  eonslanis  of  sp.vinun  h  aflet  llie  slate  of  ease 
ha.l  been  indiieed,  and  if  the  curve  for  lon-iln.linal  eompresMon  in  Ihis  he  eoin- 
with  lint  sliouii  in  li.,Miie   i  ?  ihe  -real  iiiiprovemeill  ill  the   elaslieil> 

ncsenls  loiiijitvidinal  com 


pare; 


of  the  roek  will  al  oiiee  be  -.,  i  n       In  li'^iire   i  i.  1   I 
pres^ioii  and  II  lateral  e\leiisi.,n 


gooo  ■ 

•O  700C  - 

til      i 

^     1 

Q  S0(^0 

\ 

0 

' 

/ 

\ 

3000 

^ 

^ 

'K)0 


500 


600  7O0  800 

STRAIN 


900 


lOOO 


l-l.,    \:       Sir.-  -ir.iiii  .■Mi\.-..hl,nTU(l  in  llie   lit^l  f.»u   evele- "f  oMlipri-^iuii  frnnl 
.1  eohuiiii  ..I  ll,i\en.i  -iiiiiu-,  ~liowiiiK  tlie  |in.i;res^  t,.u.iril  a  st  i'e  A  e.ise. 

CK  \Nlli:,   I'ini-KlllCAIl,  se.  .Tl.ANIl. 

A  pink  uraiiite  which  is  ahii..sl  in.listiii:<iii-hahle  fr.aii  Ihe  laly  Lake  jjramte 

ill  liaii.N])eciniensor|)..lislu. I  blocks    In  the  thin  seeli.)iis  als.)  the  resenihl      .■  ■ 

Is  VI  rv  clo-e        The  deseripli.in    -ivell  .if  the  I.ilv  Lak.-  granite    w.i'-' 

appiv  t.i  this  r..ek.  excepl  that  the  IVIerhead  -ranile  cmlainsral 

phiijioelaM'  and  les^  hi..lile     Th.'  niicr.iperlhite  al^i  is  more  Inrlml,  ii 

jrreateralleiali.m      Tlie  .piarU  aii.l  microperlhite  wliich  in  ike  np  llu    ■■  .' 

part  of  the  r.iek   liav.'  evideiitlv  crystalliA-.l  ..ill  al   about   the    saiiu  time, 

since  lliev  have  i.pialh  i;."k1  erv-,talliiie  outlines  an.l  impress  their  f..rin  up.m 

each  other  wilh  ah.Mit  e.|ual  frequeiicv      The.piartz  usually  sli.iws  pr.iii.mnced 

unduhitorv  e\linclion 

Owim;  to  its  practical  i.leiititv  with  llie  I.ilv  Lake -ranite,  in  appearance  and 

composili..ii,  it  has  been  c.usi.ler.'d  unnece-sirv  I.. -iveeitliera  photoRraph 
ol  the  p.)lished  surface  ..I  Ihe  r.iek  oi  a   phoi.ar.icni-r.iph  of   a   thin   section 


ELASTIC   CONSTANTS  OF   ROCKS. 


37 


Those  given  fnr  the  Lilv  Lake  granite  may  be  eonsidereri  as  representing  this 
rock  also  Two  s(|uare  prisms  of  the  roek  were  prepared  and  on  these  live 
sets  of  measurements  of  vertical  comjiressicm  and  two  of  lateral  expansion 
were  made       Tliese  are  given  in   the  aceoTn])anying  table,  and  the  curves 


l.iiUiiU,   l\l.rlu.i:t,  Sioll.uhl. 


No.. . . 
Size. 
Afea. 
E... 


h 

I. (MIA        1 

4,S2li,IHKl 


I   (MX. 

t,7'»n,(iu() 

(,4l.S,lKM) 


1   (Km 

Jl.S 
4.Hr)(l,(MK) 
.V4.S0,(MM) 


a 

1    IISI 
H.4(«t,(Mtn 

4,<><M).(MMt 
,\,400.(llKt 


h 


a 

998 


I    ()S2 
S,-HMt.(KMI 

.t,tlMt,(MKt 


UmKitudin.il    c<>iiipnssi..u    iiniiltiply    nadiuKs    l.y    4    for   niillifiitlisV 


I.iitiTul    fxttnsion 
iniilHimths). 


Lnail    (in 

SUli-. 

pouuils).   ! 

u. 

I.CWMI,   ,  1 

o 

J,<HH>     . 

4" 

^,(HKi.  . 

■s.s 

4,(I<K)-   . 

>-',S 

S.IKK). 

K'.S 

(i.mx).  . 

.KM) 

7,fMH>.   . 

-■!'> 

S.tKnt.  . 

J  70 

<J.(KK>      . 

,^>" 

h,IXK)      . 

2~0 

7,()0<J.   . 

245 

(I.IKK).   . 

JOS 

S.ooo.  . 

170 

4,ooo.  . 

>,?5 

J,«X>.  . 

<).') 

7,O(30.  . 

50 

I.ooo.  . 

s 

Sidf. 
V 


,0 
.so 
I  JO 

.'6(1 


Si«K'. 


4" 

s.s 
■  -'.s 
1(10 

l')S 

J-VS 
jdi. 


SicU'. 


So 
I  JO 
l(.o 

J(K) 

J.V) 
J  70 


Side. 


-4 


/eo       160       100 

S  TRAIN 


140 


o  *a         so 

Imu.  i.v — Peterhead  granite.     Slress-slrain  curves. 


!"f  I 


38 


AN    INVESTIOATKIN    INTO    TUB 


given  by  ft  are  shown  in  lifiiire  i;,     <>1"  tlu'sc  mines,  I  represents  lungitudinal 
cdinpressidii  and  II  lateral  extension 

Tile  averages  of  the  resnlts  obtained  are  as  follows: 

/•-'=  8,2<)5,(KK);         1  =  02112;         /' =  4,7<)2,(H)<):         (' =  ,^,^<)9.ooo 

The  differenee  beween  the  highest  and  lowest  values  obtained  for/'  aniouiits 
to  ,^S().(MM),  or  if  one  abnorniallv  low  deteriiiinatioii  be  oniillid  the  differ- 
ence is   I  lO.CKK) 

CRANITIC,    I.II.V    I.AKi:,    rKDVINCi:    Ol"    NICW    IIKINSWICK,    CANADA 

A  tvpieal  rather  coarse  grained  pink  granite  I'ndir  the  microscope  it  is  seen 
to  present  the  usual  liv])idioniorpliic  structure  of  this  rock,  anil  to  be  composed 
of  biotite.  microi)erlliile.  and  ipiartz  as  essential  const  it  iieiits  A  small  amount 
of  plagioclase  occurs  asanaccessorvconstiluent  There  are  also  afew  minute 
crystals  of  a  highly  <loubly  refracting  mineral  which  has  also  a  high  index  of 
refraction,  and  apparently  crystallizes  in  sipiare  prisms  This  is  probably 
zircon  or  possibiv  moiiazite 

The  feldspars  and  (piartz  preiioiiderate  largilv  The  microiHrtliitc,  which 
is  till'  most  abmid.mt  consliluent  in  the  rock,  is  coin])osed  of  a  minute  inter- 
growth  of  two  feldsi>ars,  in  neither  of  which  can  twinning  be  detected  One 
is.  ill  all  ])robabilit\ .  orthoclase  and  the  otiuralbite  The  former  is  more  or 
less  turbid  from  the  presence  of  alteration  products,  such  as  are  coinmonly 
foi'.nd  in  this  mineral  species,  while  thi'  latter  is  clear  and  fnsh  The  fjuartz 
shows  'narked  undulatorv  extinction  as  in  the  case  of  the  \\esterl\  granite. 
The  biotite  is  fresh  and  deep  brown  in  color 

This  rock  is, as  st.iled  .d)ove.a  typical  gr.inite.  rather  coarse  in  grain,  and 
which  has  undergone  but  verv  little  alteration 

A  color  process  photogra])h  of  a  polished  surfai-e  of  lh<'  rock  is  seen  in  Plate 
VII  A  and  a  ])lioloinicrograph  of  a  thin  section  magiiilied  ,V)  dianu'ters  and 
taken  bet  ween  crossed  nicols  in  polarized  light,  is  shown  in  PlateVIIli 

Two  s()uare  jirisnis  of  the  rock  were  prepared  and  their  elastic  constants 
deteriniiied      The  results  are  given  in  the  tiitie  on  page  ,V) 

The  stress  straiiicurves  given  bys])eciiiien  i  areshown  in  figure  14  Inthis 
figure  I  rep     ients  longitudinal  co..iprission  and  II  lateral  extension 

The  means  of  the  results  obtained  are  as  follows: 

£  =  8,i65,<xM);         T  =  oig8j;         /->  =  4,,si7,.SO<);         C  =  ,^,,v'^o,ocx5. 
The  difference  between  the  two  determinations  of  U  is  only  105,000. 


'I 


N 


mam 


^ 


•%■.»      .^.  w. . 


lil.ASTlC    CONSTANTS   liF    ROCKS 


39 


fliii'iilf,  l.ih  Ijike,  f'nr.inc-  »/  Xru'  Hkidku  ick,  I'liiitiila. 


Nil (J 

Size .'•'''i       ■f'is 

Arci      'J2.' 

/■; I         S.JJO.IKKI 

.._ __    i"'         2 


,|        4,'i7ll,IKIO 
.'        t„l7n,(M)0 


C 
1W5        I  05 

1    ()45  I 

8,I(I0,IKM)  I 

.I96S  > 

4.46.S,(IOO  I 


a 

— 

c 

— 

- 

....     1 

.... 

Lnnwituilitial   coiiipri-ssiini    iiiiultipK    rt>a(lin;:s 
li%    4   fur   milliiinth-^t. 


I.(i.hI  'in'ixiiiniUi. 


I 


I  ,Of)») 
2,000. 

,5,(x» . 

4,OCK>. 
5,<XK) . 
6,<l«> 
7,ooo. 

.H,(JOO . 

o,ocx> 
f.ooo. 
7.cx)o. 
A.ooo. 
,S,ooo 
4,c)oo. 
,5,ooo. 

2,000. 
I.OOO. 


-'7  t 
Vi> 


.so 
o 


I" 
,S() 
I  2n 
'SS 
Hid 
-  -S 

.■(.!> 
-•'IS 

-M4 

170 

'):r 

.so 

-4 


L.itiTj!  extt-nsioii 
iinillioiitlis). 


.V) 
.Si| 
.Si 
no 
I  I'l 
I  (■ 
150 
140 


20 


o 

1.5 
41 

fl2 

>i4 

K/i 
1,^1' 

i.s:; 

i.s.s 
'.S.S 
i.VS 
1 10 
</> 
7'* 


10 

lb 
-J 

q"  SOOO 

o 

3000 


L^i 

..^ 

k' 

K 

^ 

^ 

^ 

f^ 

u 

^ 

._. 

4iJ         «o        ..?£;        /6tT        joa       i-io      ^80 

STRA  IN 

I'll;    14 — I.ily  I. iiki' Granite.     Stress-strain  curves 


4<' 


AN    INVKSTKlATKiN-    INTO    TIIi: 


rt 


CKAMTi:,    \VI:sTI:K1.V,   KIliiDI-     ISI.ANU,    INIT     i>    -TATliS 

llii>  n  K-k  i-  ;i  Irt-sh,  vnv  Inir  ^'niiin  .1,  in:issivf,  pale  pink  i,'raiiiu-.  IkIiij;  niiirli 
limr  in  ^r^ii"  "'^i"  •'"•  "''"''  '-;'-"i''*'^  n  hrrid  to  in  iIiIn  p.ipiT 

I'ndir  till'  mirrosonpr  it  i^  .,  <  n  to  l)f  loinpoMtl  i-^SfiHially  of  biotitc,  micro 
iliiw.ortlioi-laNi,  .itkI  (iiiart/       In  aiMilioii  to  llusfoonstiluiiits  a  small  piT- 
i-inlaL,'c  oi'  pla«iodasian.la  I'rw  ,i;rains  of  nia'^'ncliti-  a'l-  priM'iil  as  aivi-ssorv 
lon^tilnints.   loj,u.tlK.r  with  a   litlU    ililoritc  and    mnscovitc    as    altiration 
]>ro(hnts 

Tlu  tildspar-  I'onu  tlir  ynatir  part  oi  llu-  nuk.  miiToi-lini' lu'ins  l>y  fartlu' 
most  ahnndant  of  iIrm-  li  allows  in  a  slrikini;  nianiur  the  cliaractcristii- 
cnKs  liatclud  twinning  of  llii-, -.piiits,  and  is  nsnallv  (piilr  frisli  The  ortho 
dasc-  in  untuimuil  individuals  is  fri(|ni!illv  distin.'tlv  turbid  from  the 
dtvilopmiiit  of  kaolin,  and  in  a  frw  l)lai'tsninso)\  itc  in  larf,'ir  individuals  lan 
Ijo  si'iu  inclosed  in  it,  api)arinllv  divilopin«  as  a  secondary  i)rodnit  at  its 

expense 

The  <piarlz,  uliieh  is  next  in  alnmdanee,  u>n  lUv  nIiows  marked  undnlitory 
extinction,  and  some  ,s,'ranis  have  been  so  strained  that  thev  fall  into  areas  with 
dislinetlv  different  optical  orientations  The  (piartz,  instead  of  occupviuK 
corners  between  the  feldspar  individuals,  nsualh  occurs  as  subanjjuUir  or 
more  or  less  ronnde<l  grains  associated  with  the  feldsi)ar,  and  apparently 
more  Tiearh  contemporaneous  with  this  mineral  in  its  crystallization  than 
is  usi'.dlv  theca-e  The  rock  often  shows  a  tendency  to  Kraiiophyric  struc- 
Inre,  small  rotmded  (grains  or  verTuiform  iuclnsions  of  cpiartz  being  sometimes 
seen  inlhe  microcline  Tliestructnre  otherwise  is  of  tin- normal  j;ranite  type 
The  bioliteis  very  subordinate  in  amount  and  is  more  or  less  chatiKed  into 
chlorite 

.\lthoui,di  these  dec<  imi)osition  iirodncts  are  present , the  rock  can  not  be  con- 
sidere<l  as  (me  which  has  undergone  much  alterati(.n  11  has,  as  a  matter  ol 
fact,  \mder^jone  vi  rv  little,  and  is  to  be  elas>ed  as  a  distinctly  fresh  rock  luuch 
fresher  than  ijranites  usn.dly  are 

A  color  process  photoijraph  of  the  rock  isseen  in  Plate  VIII  A  and  a  photo- 
niicroi;raph  of  a  thin  section  taken  between  crossed  nicols  in  jxilarized  lii,dil 
and  masnilied  ;,()  dianuters  is  shown  in  Plate  \'!II  n. 

I'onr  test  jiiices  were  used  in  measuring  the  elastic  constants,  viz,  two  stpiare 
prisms.  II  and/),  and  two  round  columns,  r  and  ./  Two  sets  of  determinations 
.veremadcoueachofllK  first  three  specimens,  the  instrnnieiits  being  attached 
I.I  different  pairs  of  sides  in  each  e;isi',  and  four  sets  of  delerminations  were 
made  on  specimen  Jin  planes  making  angles  at  45°  witti  one  another  Ten 
determinations  of  vertical  compression  and  three  of  lateral  extension  were 
thus  made  the  results  of  which  are  given  in  the  following  table: 


B       ^MOiOMiCROCiMAPH   Of-     liN   SECTION,  Ix   30   0t*M.-NCOL3   CROSSED^ 

GH4Nl'"R,    WLStLRl/,    ^-iHJlliE     ISLAND. 


\ 


Kl.ASTIC    (.mNsT ANTS    oF    kocKS 


41 


Cr.iiilU-.   \\,~l,rly.l<li'.l,l.l.in.l.  V   S     \ 


Vii. 

\        " 

II 

h         1 

h 

(■ 

i' 

it 

St/r 

I   (W»S          1   '»>2 

IJMI 

'I!') 

'»M 

T,  s 

Aril 

1     III 

Ill 

7^ 

1            TS 

>mU' 

( 

r 

r 

/* 

'  h..U  . 

M  \u 

l.-s        tst    llnl 

/., 

7.1M1.IIIHI 

yi  1011,11 

Kt 

.' 

2h  III  HI 

"  7)S 

HHI 

7  »,;.( iHiii 

■  t ;  ^ 

HMl     ,,S7'4,"" 

1     «  ■ 

.'1 

I'lHt 

Jll 

-M 

1 

1             -  -*  ^ 

:    II 

4.nii,i"«i 

1  ij^ii  •> 

Ml 

1  ■ 

..,l«,„ 

t    >|-' 

...n 

4/,iin.>i 

' 

.>'.;ii.iB..i 

,'  'Kill  Ih 

Ml 

i.l 

•  TO.IUH) 

(   IKS 

, 

tll'KMH 

! 

•il  hi.lis      111  lic.li  ,    Ith   li.iU-^ 

7    ^^  IMiii    7   1  7m  IK"'  7,iSll,(MMt 
I  diIKH)  4.l2lMMHt;4..140.(KMIi 

1 

>  ilSd  IIIMI    .11)111  l>INl!.Vl>'>l,INKI 


I  I    IMS  VI      V  .'VIIWI 


Ml  Mill'.    t<i  \i.r..;i   iiv    t   t'-tt   Mil  I  I"*.  Ills 


|.|I,..U-     Mil..!..     I-II...I.,     J.lh.l.-     Ill  lu.l.s   ^lll   lii.loi 


l.rNHi 

i> 

J,(MM>    1 

V> 

,;.(KHt 

t*^ 

i.iXN-. 

1  )■• 

>.'««> 

i>. . 

(t,IMM> 

-  -  s 

7.(H  Ml 

-■'•S 

>.I»(MI 

,1'tS 

«>,I«M» 

.ui 

S,tKM> 

.^n» 

7,(KKI     ' 

J7<» 

fi,(MMI     . 

-'  1 S 

5,(MH1 

Jt  M  » 

.(,.Hk. 

r(ii. 

;,iMH» 

1  ii> 

1 

IMHt 

2 

(MHI 

} 

ntH> 

4 

(HM> 

S 

<HMf 

() 

mm 

mn* 

s 

IHtO 

<) 

1 104  1 

s 

udi) 

7 

INMI 

6 

(MM> 

5 

iXM) 

4 

(KH) 

.\ 

<HH) 

.' 

ni » 1 

I 

ix>o 

t 

1' 

llMt 

1  Jt 

1  S<i 

!'i. 

l<f(> 

-■  r* 

-'  ;s 

:>K 

-'7  S 

.^^!! 

I'lS 

I    MIKAI      |-:xrKN*HlN  -    MllLlllNUM 


l.(i:ul     ill  |><it:n(l< 


1   I*! 


H"  4^,1   '        -4''5 


,V)0  ;       ,<i>5 


,l'>i 


1  15 


I  4'>  '  V> 

! 
lo  i  IS 


a      I     h 
i.mn  i     929 


A" 
5" 


KHl 

1-5 

1,(1) 

1  77 

Il)<) 

-•-•O 

li)S 

■  '..s     . 

14"     ! 

177 

I  IS 

I  ;5 

1)1) 

KX) 

■44 

4()0 

.W).S 

140 
12 

.97.1 


.V> 

.So 

I.>(> 

I7S 


20f) 

1(1.1 
I.V) 

6o  70  <)<» 

M>     i       .^o     i       4.5 


vr»* 


42 


AN    INVICSTH.ATIOV    r.TO   THK 


1 


w 


The  slrrss-Ktrain  .•urvi>  ..btaima  l"r..m  spiv  imeu  ..  i.^,.  ^ivon  in         ix-  i  s 
Inthis  r.«urf.I  r.|>r.sints  l..nKitli<linal  co,m|...  ssi..n  .iml  11  lat.ral  •        nM.m 


■rooc  ■ 


sooo 


3000 


lOOO 


— 


t  \    "T 


y  -^ 


1 

3?0 


Till-  aviT,ii;>-.  of  Ha  v.iUi.-    ■>!il  niu'l  are  as  fallows; 

i:   .;,.,, .5.-:  .  '■■)5.  /'-4.V.70-.;  ^■"■"■.   -■ 

I'lu-  iHlTcRiK.  ,  1.  uvi.M  iJic  liii,'!i'-t  am!  !,>wc>l  val.KS  ..1  'iir  <1.  "   •  . 

,MU,,ns..|  /'„n.,».nm.>,  ,/w,..o„lv.s,,,K.,        Mf  ,1,.    .tin-.         -nns        ..iv 
,„i    111  ;ivcni-r  sniiu-wli.it  lowri,    mil '•       iiuuli.i       iijli      nsiill- 

I.RS\    11;      •>rlM-Y.    \I.\SSAClirs';TT-,    UNITi;.-        lATK^ 

TiK   :'.rk  is  ;.  ■  .tiuT  o   irsc  ;;r.;i.ic<l  i;r  ,v  uraniti-  c..nM--«-'l  -        *-'r^''^'  '^| 
,„uT„,    ■!lnuan.l.|n.irtz      Tlic-  i...n  ma:,'.u -,  -  -  ...istitiK-i,.-.   ^.n         .resent.^ 
l.vav. -..Kv,.  n.alinn  ■  l,hu-k.h..nil.U.    .      ,ss..u    u-..    vitli        ;>li  '  ic 

n..H.arstol,fav.   !U.  am.Miul.)..  v.r    -Uu .   -.Innd  ,>   r,.--    ne       1  lies. 
....ustitiu'iils  h.-l..,„  I..  i!u  alkali  ri.  !i  v.iruti.      -.  ilu-ir  r.  ,,hcI  r- <■  tainilu- 
■,„•  s..  opaiiuc  ih.il  it  is  .liltkul'   In  .Ut.rnii      auirpr.    ise  clian.cttr 
..,,,K      ,.,'irr.«uUrin.lu.p.',n.H'        .,0.       -    >..-^. -n  th.      '  Isparsram 
.,,,1,    .,1,   ,",utralc<llu    crvst.iU  !..■  mu-i  ,hnuin.    'liat    ^u-^ 

.,  ,m,.u.i    ■■.tlatc-r  tlia.i    ho  iVMsp  Tii.   ^-  -tn,.r         Inlat-.r 

i-xtiiiftion       riif  rock  is  ii'  -li  an-        lalliri 

A  color  process  photoK-rapl.  o,  .lisl.  u  ■     .  .'un..      .ruuile  is 

4iownin  Plate  IX  A,  ami  a  phn.     auroKraph,.       ih.a  sec;    m  .ukci  Letween 
crosscl  nn   .Is  in  pnlari«-.l  lii^tU  a,,!  nniKiufied  ..dian    'crs  1-.  reproci--tHl  in 

rlatc  iXii 
Two  large  s,K-ciiiun~.,{  the  rock,      .ich  li.lTcrc.l  sli.       ■  fnmi  om    ,>■        - 

anmaranc.    .vere  secured  and  exar        d       llm-c  -o.   ire  pnsms,  a,  c 

^4-  pr.-  -.1  from  .•■•nr  -specimen  a        -.  srpian-   pnsra,  b.  from   the      iher 


%- 


•^  , 


«e& 


ii.lv  of 

■Sflltl ■' 


lati. 


mile  IS 


••<1  in 


lUllT 


■i 


ELASTIC    CONSTANTS   OF    ROCKS 


43 


Granili,  Quincy,  Maaiichu^ilh,  I'liil,'!  Slatr 


I'ir'-t  s 

iH'cinu-n. 

SditiHl  -pi-cinipn. 

Ka 

(1 

(( 

r 

r 

,/     1 

./ 

/. 

b 

Si/e 

.ystj     1.(171 

l,(lf..(           OSS 

1   1111            '(S4 

'14  s        »>I2 

Area , . 

1  (>(> 

1   m. 

1  111 

1  01 

')(,.S 

<tf..S 

K4-1 

84.1 

K 

6,.5W).(KM) 

(t..S|l»,ll(H) 

(i,f>lM.(MM) 

(..(.((l.IMM) 

(i.Hid.iKMl 

7,(MNI,IMm 

S.l  ts  (HIM 

H..t(>ll,(H)0 

*..... 

18,S 

IV.'.'i 

.'1 

21 

244 

^■i 

I"*1S 

2I>4 

n 

J,47(1.0()(l 
2,7ft5.(HK> 

.»,7l(l,(HH) 
2.H(..S.()(«l 

.t.Kll).(XM) 
T,7(,<1  IHMI 

.t.KHl.lWlO 
2,7(i(l,(MI(l 

4.44I1.I1(H1 
2, 74(1, (MM) 

2,H(«),(HMf 

4. 1'^D.IMMI 
.(.4l(i.(l(KI 

4,72(l,iHK) 

f 

.l,4«il.lH)0   ; 

Ia>ngiti:i>inai 

C<>.Mi'l(l:-ssl(i.N 
Side 

-MuLTii'LV  Re 
Side 

APINGS    HV  4  PI 

Side 

R   MiLLtoNTllS. 

Side        ,;        Side 

Side 

Load  (in 

Side 

Side 

pounds). 
1,000 

U. 

0 

U. 
0 

P. 
0 

V. 

P. 

u. 
0 

P. 

0 

0 

0 

0 

2,000 

60 

5" 

S'' 

4.S 

50 

3,000 

1 10 

>).'> 

1(«) 

I(X) 

I(X> 

4,fxx> 

160 

'45 

■III 

'5" 

142 

■i,OlX) 

2(X) 

■  85 

206 

,<JH 

193 

0,<xxj 

240 

2.10 

2.S') 

246 

225 

7, (XX) 

280 

270 

291 

2(^) 

260 

H,ooo 

.UO 

310 

^^4 

3.10 

WO 

<),liOO 

360 

,U.S 

.^74 

374 

380 

370 

.      M>5 

355 

H,ooo 

,?^> 

MS 

.v.s 

340 

314 

7,000 

282 

280 

2(K> 

298 

1     .... 

274 

6,000 

HS 

2.VS 

2'l( ) 

2.150 

.... 

.... 

235 

5,000 

-'o.i 

■  '(.S 

210 

210 

I()0 

1  4,000 

162 

140 

.'.,s 

If'.S 

145 

^,000 

112 

()0 

1  in 

■■5 

.... 

1     .... 

100 

2,000 

6., 

1" 

60 

.... 

to 

.... 

50 

1,000 

4 

,s 

5 

° 

.S 

5 

3 

5 

Lateral 

HXTESSION  -  J 

lIlLLIONTlIS. 

rst  specimtn. 
0 

K-t.-iiiicn. 

a 

.9(0 

0 

d 

1  nil 

0 

1        Scinini  s 

1     No.. . 

■■-'1 

b 

892 
0 

b 

.94S 
0 

-■■    ■       --  — 

1 

1,000 

2S 

3^ 

24 

20 

'     .^.o*x» 

4,(HM» 

S,5 

70 

SI 

45 

210 

CJO 

H5 
I4S 
17.S 
200 

24" 
20.S 
180 
I.S.S 

1 10 
l.so 
IiK> 
2.iO 

270 

-•75 
240 

i<»5 
"55 

7<i 
1(11 
1  -vs 
i,S7 
174 

20f> 

'         >75 
153 

i         127 
i"3 

KM) 
I-VS 
155 
I  Ml 
219 
192 
164 

.*^  (KM) 

.S.fXM) 

'34 

j        .^.(NM* 
i        4,0(X) 

'Oi 

95 

12U 

77 

88 

1        ,1,000 
2,000 
1,000 

60 

75 

50 

50 

j 

30 

40 

35 

25 

,5 

5 

10 

2 

3 

44 


AN    IN\  i:sriC.\T|il\    INlcl   Tin: 


i 


spi'ciiiun.    uliii'li    was    ratlitr  ihirkiT  in    i-olur      '{'\\n  sirii's  of  cntnprcssiim 
(liti  riiiiiialinus  urn-  ninli'  nii  t;uli  nf  llusi- [iiiMiis.    I{ij;lit  siricsof  nuasiin 
iiKiits  ui  II'  t!iii>  iiiadi-  111'  MTtical  oniipris^inii  ami  li\  i'  of  laUral  t'NU'ii>iiiii 

III  llic  sii-(iii(l  spciiauii  iif '111' rin'k,  /'  u.is  fdiiiid  In  luivc  a  ratliir  liii;lu'r 
valm-  lliaii  in  lli'.'  casi  nf  llu  lir-l  "-pi-ciiiuii,  alllioiiHli  prism  ■/,  fill  fioni  tin-  first 
iipt'ciini'ii,  ap])niaclu's  this  valiu'  dosdv  Tlii'  iliiplicati'  ik'tiriiiinatiiiiis  iiuuk- 
iiiu-ai'li  'i\  tln'  prisms a'^ri'f  vcrv  cliisi.'l\  uilli  oiu'  anntlirr  Tho  rt'Siilts  nf 
till-  im'asiin.'iiu  Ills  arr  ,i;i\rii  in   llu-  talili'uii  paj;i' 44 

riif  avi'raijf  of  IIk'  valius  nblaiiR-d  in  tlii'  case  (if  llie  first  spccinuii  are  as 
f(ill.iu>: 

/'.       '1.7  |.7.'i'>  >;  ■'    -I) -MS-';  /'  -   ;.')>!4.i)i)<):  C --  -;,7Mi.6<ki. 

TIr-  awri'^H-  "i  tli'Ki-  nhlaini'ii  Ir  lai  tin.-  sfcoiul  speoiiiU'ii  are  as  follinvs: 
/•,'  -  S,j47.,si»i;         ■^-^•111)77;         /'      4.5s5.'«ni;         C"  =  ,^,44,s,(hm). 

In  this  ease,  as  has  ln'eii  nieiiticmed.  the  Uvn  speeimeiis  represe.it  different 
varielicsnf  the  (^iiine\  .t;raiiiti'  The  stress  strain  eiir\i'  yiveii  bv  speeinuii  /' 
is  sh"uii  in  l"iL;iire  1(1  In  this  l"!i;iire.  I  repn-si  ills  liin,i;iliidiiial  eiimpression 
and  II  lateral  exlinsidii. 


I 


I'l'.    If)      <^luitu'\- CiruiiK'.      Slrt'^^  str.ilti  cnr\es, 

(.K.wiii:.  --rwsTi;  \i).  PKiixiNct;  ui'  iiri'MitX',  c\n\i)\ 

This  is  ,1  line  ^rraiiud  ;,'ray  kt-"!''*'.  "liieh  (ueiirs  as  a  Iari;e  itilnisivc 
iiiasseiilliii','  s|;  tanf  Iciu-er  I'aleo/oie  aije  It  is  exlensivelv  (piarried  and  is 
IarL,'el\  ii^ed  as  Iniildiii','  inaleri  il  and  fur  pasiie;  si'ts  in  the  eilvnf  MDiitreal 

II  is  liintilc  iiiiisi'i)\ile  granite,  liavini;  as  its  essentia!  eniistitiients  iirtlio- 
eUise.  (piarl/',  and  hintile,  hut  eoiitainiUj;  also  a  rather  small  aiiKUint  nf 
iniiseo\  ite  and  epidute,  both  (if  which  (iceiir  as  skelelmi  ervstals  of  consider 
able  dimensions,  for  tlie  most  part  ijrowiiii;  in  the  feldspar  aiwl  apparenlK- 
of  secoiuhirv  ori'^in  The  rock  is  verv  fresii,  beiiii;  almost  eiilirelv  fre(  f  'H 
the  usual  decoiiiposilioii  pr'>ducts      In  addition  to  orlhoclase,  the  rock     a' 


\ 


KI.ASTIC    CONSTANTS   OF    ROCKS 


45 


tains  a  coiisidcralilc  pcroontaKc  of  tiiicrnclim-  and  of  a  plaRioclaso  of  tlic 
soda  linu'  sirics  Tlii'  mica  is  nla lively  more  al)'.indaiit  lliaii  in  llir  oilier 
granites  dcscrilHcl  in  the  prcsiiil  ])ai)er  'I'lie  (jiiart/  allows  marked  undii- 
latorv  extinction  and  in  some  cases  even  an  incipient  jjranulation  Tlie  si/e 
of  the  jjrain  of  this  rock  is  intermediate  between  that  of  the  \\'csterl\-  and 
tlie  other  granites,  which  latter  are  themselves  ahont  ecpiallv  coarse 

The  elastic  constants  were  measured  on  three  stpiare  prisms,  four  sets  of 
measurements  of  verlicai  eoni])ression  and  three  of  lateral  extension  being 
made      The  results  are  given  in  the  following  table: 


(iriinili,  Shinsli-ail,  /'ruMiic    i>/   Oiiihn,   Ciiiiilila. 


No 

a 

Sue.     , 
Area 

.9S4         .M 
.  9(W» 

Side 

U 

6.000.000 

» 

.253 

I) 

4.040.1)00 

c 

2..i95,IH«. 

b      \       h       \ 

1  ,(HS       1  .(«X)9      I  .Ol.-i        I  .(MM)*>H 


1    (110 
(• 
S.d.tO.OOO 

.251 
.?..i60,000 
2.015.000 


I    lllr, 

;'. 

5.540.000 

.282 
4.250,0<M) 
2,155,(K)0 


roos.*    ■    .957 

.  965 

I  .... 

I  6,170,000 

.248 

4.110.000 

2,470,000 


LonKitudinul  cf>mpresston  (multiply  readinfs  by  4  for  millionths). 


I-oad  (in 
pounds). 

i,0()n 

0 

2,ooo 

70 

,l,rx)(> 

i,vs 

.4  ,(XX1 

2(X» 

sj.rKMI 

-,sn 

f).(XX> 

.V'> 

7,(KK> 

y.o 

S,(XX1 

41s 

,        »),(KM1 

460 

S.OOO 

7,f»(i(i 

6,rKx> 

4,f)no 

2-M> 

,!,<»<  K) 

160 

.\(XK) 

()<> 

I.fXX) 

in 

mo 
J  so 


.|')o 

tt" 

.<So 

,u.s 
1'I5 

l-'S 
lU 


7,S 
"  t.s 

J(XJ 

-M.S 
.*o.S 

44.^ 


o 

60 

I2.S 
iSO 

-\?" 
2S0 

420 

-").s 

2.S" 
2fX) 
14" 

«o 

2 


a 

954 


b    I 

1.015 


.957 


I.atcriil  extension 
(millionths). 


20 

,1" 

40 

(11 

7" 

.So 

l"S 

I-'.S 

III) 

>w 

ISO 

'.S.S 

2(K1 

2»0 

iq.s 

2.tfi 

280 

2,15 

^OS 

,1,VS 

27.'i 

.vs.s 

400 

120 

.t-'o 

.M" 

-''l.l 

27.S 

.'■)<) 

2<1,S 

2.(0 

25(1 

2.<0 

LSI) 

100 

201) 

M" 

i,;o 

if^iO 

<»" 

70 

1  10 

4.S 

.;n 

.SO 

~5 

-., 

■5 

The  averages  of  tlie  results  obtained  are  as  follows : 

/;  =  5,6,Ss,oo();        "   =0  2,sH5;        /.  =^  .;,i;4i>. <'<><>;        (    =   2,258,700. 

This  rock,  as  will  lie  seen,  has  a  low  modnltisof  elasticity,  and  likeother 
rocks  of  which  this  is  true,  the  lateral  extension  varies  considerably  in  different 
specimens  and  the  rock  does  not  come  readily  to  a  state  of  ease.     This  is  seen 


dB 


46 


AN    INVI'STir.ATION    INTO    THK 


fr..„,  f.Kure  .7,  ^^l.u•l.  slunvs  the  results  ol.udncl  in  tlie  first  tl,r..  ovc-U-s  --f 
,  ,n^si„„  „K..U.  upon  a  clunn,  ot  .h.  rock  llu  hvM.ros.s  sl,n.„  ,s 
\Ju  ,n,,u.  .]K,n  in  .1,.  ..s.  of  :nn  of  ,„.■  o,l,.r  cr.^  s,:.Ihnc.  rocU 
.xan,in.d.n,d.v.„  after  repeated  strc-ssn,,. his  l,vs,.vs,s.l..,on..r..ln^^^^^ 
does  not  disappear,  as  is  seen  fro.n  the  curve  o,  the  results  ohta  ..ed  f  n 
cohuun  „  .dveu  in  ll.nre  ,8.  In  this  f,«ure  1  represents  lon^.trnhnal  co  .^^ 
press.ou  and  II  lateral  esteusiou  The  variation  iu  the  results  ol.tan.ed  for 
/;  aeeordinuK  i>  hi;;h.  auiountin-  to  S.,o,...k) 


9000 


1000 


200 


300 


400  500  600 

STRAIN 


70O 


800 


,.■„  ,  -  Stress-s,n,i..  cnrves  .,l,t;,me<l  in  the  f\rsl  three  .  ycles  „f  o.,.;,|.re.si.,n,  from 
'  ;,  o'lninn  ..f  SlMiislea.i  Granite,  shiiwinn  ns  initicrfeot  elasticity. 
(,„  account  of  iis  defeaive  elasticitv  the  res.dt  of  the  tneasurctuent  of 
,he  con.pressibilitv  of  this  rock  is  less  satisfactorv  than  that  of  the  other 
Krat.ites  from  which  it  differs  consi.leral.lv  in  the  value  obtained  for  /^. 
,Uh.m,h  the  values  obtained  in  the  case  of  the  other  «ranites  a^ree  pre  y 
clos.lv  anton,'  thetus.lves  The  c.use  of  this  defectne  elast.c.tv  in  the 
Stattstead  «ra"ite  is  no,  clear.  althoUKh  it  tnav  be  cmnceted  wtth  a  luck 
of  strength  n,  the  rock,  which  in  itsturt.u.av  1...  connected  wtth  the  presence 
in  the  rock  of  so  laik'e  an  atuount  of  mica 

I,  is  a  weak  rock  compare.l  with  other  f;ra..itcs  or  with  the  essex.te  from 

M„u.U  loht.sou.  as  shown  bv  the  results  of  a  series  .,f  testsca^ned  out  in  the 

Testiif"  I  iboratorv  of  McC.ll  rniversitv.  atid  siven  in  the  table  on  page  47 

A  colo^  process  photograph  of  a  poHshe.I  surface  of   the  rock  is  shown  .n 

Plate  K  \  and  the  photomicrograph  of  a  thin  section  of  it  in  Plate  X  b.     1  ms 


(jRANiTE     ST»NSIE«D,     'kUtrA. 


Jfe  "M  *S 


i 


I 


ELASTIC   CONSTANTS   l)F    ROCKS 


47 


/ii/'/f  v//i'ujni;  (omf'*italr.i-  ^tt*  in^^th  nj  St<in4ttiil  (irtimff. 


Granite, 
St.  Pliilip,  iJiuUi 


Ari;i      WilKllt 


Attn  il  I  i'ld  i«T  Miix. 

Ill.ltl  .It  ^>|   111   .It  Mjx.  ,ouU 

iiiili.il        1111(1. tl  Iliad         iMT  sq 
fiiiluri        t.iilurt-.  I    inclt. 


'    1  J  S'l  liy  .'.^i  liv  .','•(.  'I    =;-•- 

( /.'  -•  t;  li\  .'  )(i  li>   .■  5-'  ''  ' 


Ksscxitr.  <  1  -■  (7  t'v  j  (i>  liv  .■  ,j  (.  f 

Mt.  JiihiiMiii.fJtiilm-  I /;  .'..(N  liv  .•  ^1.  Iiy  _•  s<' ''    ;■ 


■^    [It.cxKi    I7.;i(i    I  ?_(,.t<Kt  IH,()40 
i|i;,ii<«>  i.^.ii.'ii    ■.-i.',>i<K>  J,?..V)0 

1 
I  ;.'^.m»i  .'<•  ■  HI     1  t^,7iK)  2J.)'>5. 
1.^1, (xKi  -'j.rii     i'i7,7(^»  26.,;a4 


Granite,  (    1  .•  fn  liv  _•  mi  li>  -•,  ^.' '•  ,S-'>  i    SI15       i|.'.7i« 

Stanstiad,  IJiii-ln-i-    .  \  /;  .'.5(1  l.v  .'.55  liv  .>.47  d.  ,s.'>  i    sii       NN..iix 


«)J,7(K>  14.206 
Si;. 300  13,526 


■; 


latter  is  taken  in  oniinary  liijlit  and  inaKniliid  -•;  ilianutiTs  Tlic  fact  that  this 
photoinicrot^raph  is  takin  in  (irdinary  lij,'ht,  uhilt-  tliosi'  of  ntliiT  granites 
just  discriljfd  arc  taki-n  bitwecii  im^si-d  nicols,  ^'iyi-s  this  rock  an  appear 
ance  of  being  coarsirin  grain  than  il  really  is,  owing  to  the  honndaries  of 
the  colorless  constituents  being  ill  delined  The  >ize  of  the  grain  may  be 
seen,  however,  by  comparing  the  diniensitmsof  theiron magnesia  constituents 
(M  the  rocks  or  still  better  by  com])arit!g  the  gi  ain  of  the  several  rocks  as  shown 
in  the  ])hotographs  of  the  polished  surfaces 


ao        I20        ISO       zoo       no       zao      3zo       ^to 

.1  TRAIN 
I'"|(i.  iS. — Staiistead  (iraiiite.     Stress-straiti  curves 


NEPHELINF.  SYENITE 
NHPIIEI.INR  SVKMTl!,  COKroKATION  ol'ARRV.   M(  iNTKK  Al,,  CANADA 

This  is  a  typical  nephelinc  syenite  which  forms  a  portion  of  Mount  Royal, 
one  of  the  .VIontcregian  Hills  ami  which  cuts  an  e;irlier  intrusion  of  esse.xite 
like  that  to  he  described  later  from  Mount  Johnson 

It  is  a  hard  and  tough  rock  used  as  road  metal  on  the  streets  of  the  city  of 
Montreal.     It  is  rather  light  gray  in  color  and  often  shows  locally  a  more 


I 


\N    INVKSTir.ATIDN    INTO  THK 
is  also  ,,ns.n,  in  „o.  -K-ou.wUral.l.  '""'"'         ;".^.„„,„    ,,-  UKMUon-r  Uss 


Q  av  ■"'  STRAIN 


Z80 


fl.,,a.  s,n,cu.re  a,.,.v.  nK.n.i,.,,...  r.-suhs      As«^t.c,  with  J^^  ;;^;«;;.-,;; 
ncplHlinc   in   r.alur  s.nall   a.noun,,  an.l   also   "-■'"'        ;;'f^,„,,,,,      ,„ 

:£,  Uav.  „v..naU.„  ..,...,  ...  .,ui..  i^        ^f  i;;;;' -[^^.t     XI ..  an.. 

v., .lor  process  ,.hoto>,ra,,l.  of  a  r-''^-     ^^'^^''\  '^  ^""  '"  ,    I.,,     ,,  ,  i,,„. 

a  photon 'icrograph  taken  bctwc.-n    crov.  •  mcols  and  ntagn.tu.l  ,,  .  .hant 

tiers  IS  shown  in  Plate  XI  u. 


TOMCROURAPh    Ot     ■-■<:U   SECnON,  (x   30   D^AV.- NXOl.^    CROSSED^ 
NfcPHELiNt    SYFNirr,    V  ;NTftfAL,    CANADA, 


i 


KI.ASTIC    CONSTANTS    OP    RDCKS 


40 


Tw.i  S.IS  of  Ml.  iMir.uuiits  lor  Ihf  ,l,isli.-innstimts  wire  tna.I.'  ..n  a  >iiiKle 
s<|iiaro  |.ii>M.o|-  tlir  VK-k.  Msiii-  lir-toiu'  mI  n|  liioi-s  ;in.l  tli.n  iIicoHkt  The 
rt'sulls  art  M-t  loiili  in  ilu  h.ll.nMii.;  l.iMc; 

\,l-li.!iti'    '^l.«'^      \l„iilr,.ll.  I  ilml.lil. 


II 


il 


\r..i 
ft  . 


I  1    .Ml 

1    r..ii  1 

'I. Ml 1. lis  mill 


i    o 


■('» 


i>,  isii  itoo 
(  \ ;  s  I  III!  1 


I  l.liIluilUllilLlli !■     -11.11     IMlllllliK    fl    "l"l>.'- 

I.\    1  ft.r  iiiilli..iitlt>  . 


I  1^1. Ill    .III     IMUlIll].- 


4.I' 
S.I 
'i.i 


Mill' 


-.fHKl 
,OtMl 
.fMXl. 

,ooo 

,(XXJ 
,0<X) 
.(KX) 
,(KX> 
.l)*K1 


I'lS 

-',vt 

Id 

14" 
loo 

7n 


'IS 

I7*> 
-'"5 
:!4.S 
-7S 
-MO 
^lo 
17" 
140 


11 


I.ittrr.il  i-xtcnsiiin 
iniilli..iilli... 


I 


l"S 

I.i" 

Ifio 

i.>^=; 

-•Id 

HI" 

i''5 

t^s 
1 10 

«S 
S.S 
,1" 


- .) 
Si 

1 10 

1  IS 
ITS 
.'(to 
-  (" 

J"0 
ISO 

1S5 
1-5 

'»S 
''S 

.ss 
5 


The  stress  St  n  in  curves  ohliiiu  .1  in  the  first  si'l  of  itiea^urements  are  seen 
i„  Il  ,  ,,  ,,  4S).  in  whieh  !  represents  lonsitudinal  coiupresMon  and  II 
-hows  laural  extension  An  exaniiiuition  of  these  will  show  that  the  rock 
.  Uiihits  very  little  hvsteresis,  the  v.ilius  for  l(m«ilii.litial  compression  fiivijig 
a  straight  line,  a>  in  the  case  of  wroni;1it  iron  and  other  metals 

The  averages  of  the  results  obtained  are  as  follows : 

/•;-<).  I, w. .SIX';         "-oj.s*).         /'=- f>,-\^7..s™>;         ("- ,v6(,s.'KX) 

Til.  (iilTerencesliet  ween  the  iwoiUl.nninalions  for  the  value  of /^  amounted 
to  only  2.\^.i«K.  piuin.ls  As  will  he  ol.  rved,  the  value  of  D  for  this  rock  is 
much  higher  than  that  for  any  of  the  granites. 


so 


AN   IWESTir.ATION   INTO  THK 


!    I' 


BASIC  PLUTONIC  KOCKS 

WMKTII'isl  II.,    \i:\v  l,l.\sr.i,u,   I'KiiMMi;  ill;  >ili;iPi:c,   CANADA 

I  111-.  rmV,  In  III. Ill  till  i;n.il  Miiiiii  :iinirtlii.sii(  iiilrii>iiiii  wliiili  (iciiipiis 
ail  .ircii  ipf  i,iH>  si|ii;irc  luilis  mi  ilii-  luiriUr  ul  the  I.MitrinliHii  iinil^ixis, 
M.iM.  (,)  niilis  iii.nli  III  till'  ,itv  nf  .Mmilnul*  Tlic  ~|«iiimii  i-,  fmm  llif 
iiiaryiii  nf  llic  iiilrii-.il III.  «lur<-  llic  miss  Ii.is  iiiiiUijjnm  i Alciisixt-  iiiiivciiiciit 
111  ilu  iwliiri' III  rorklliiu  whiili  iiium  nuin  li.is  tutu  linnitilit  about  liy 
|)i  -lire.'  ixcrti'il  iipiiii  liic  i-.irlli's  iriisl  in  tliis  distriii  Tin.  fluw  has 
lak.  II  [ilicc  tliriMii;li  a  j,'r  niiilaliuii  ul'  tin.  Luiicr  iiidix  iduals  <i|"  llu  original 
mrk.  iiitiiliiiicil  uiili  a  iiiiivfiiiftit  uf  Uiis  ^r  iiiiilalril  iiiatirial  iiiidtr  IIic 
iiilliuiKi  iif  the  imssuri-,  i,'i\iii),>  risf  in  a  riidi'  liandini;  in  t\w  rmk  This 
Kraiiiilaliiiii  has  iinl.  ImwcviT.  hi'i'ii  a(.'oiiii[)aiiii'd  liv  aii\'  Inss  uf  slriiij;th,  for 
thtrmk  is  a  hard  and  i  \.tiMliiii;l\  Iniiijli  oiic.  hiiiij;  used  as  paving  sets  in 
siiim-  of  the  strit  ts  in  the  city  of  Mcmtrral,  wliiff  thiTt-  is  an  fsi«ciallv  heavy 
trallic 

Most  of  the  Morin  intrusion  consists  almost  exchisivel\  nt  plagioclase 
felilspar.  whieli  lias  the  eoiiiposition  of  lahradorite.  with  onlv  a  \er\  snuill 
[Hirlionof  iron  iiiai,'iiesi;i  eonstituiiits,  and  lieiue  the  roek  is  projierly  termed 
"aiiorlhosile  " 

The  speeinun  used  for  the  detirmination  ui  die  elaslie  constants  of  tlie 
rock  wa-  t  iit  frmii  a  paviiii,'  set  wliich  was  richer  tlian  usual  in  the  iron 
inaj^nisi;!  i  imslitmiils  .md  whirli  luiiseipienlly  mi>;ht  he  more  properly 
referred  to  as  j,'al)hro,  althoinjli  il  is  iiii  reha  part  of  the  Miorlhosile  locally 
1:  'ler  in  I hese  darker  constituents  It  li  is  u  riideU  streaked  structure,  as 
Men  III  the  accoiiipaiiviiv;;  color  process  photo^'raph  of  a  polished  specimen 
Plate. \n  \  This  si  riicture  crossed  the  vertical  face  of  the  test  piece  diag- 
onally, SI,  that  if  llurc  he  a  \ariation  in  the  \.iliies  of  ihe  elastic  constants 
dependent  on  the  direction  of  the  streaking,  the  readings  attained  will 
rejiresent  a  mean,  or  at  aiiv  rate  an  intermediate  value 

ruder  the  microscope  the  rock  is  seen  tobe  con.jxised  chieliv  of  pla,i;iocl.,  o, 
associated  with  which  is  a  pale  jjreen  aiifjite,  a  deep  E;reen  hornbluMle,  with  a 
feu  grains  of  ihiienite,  and  an  occasional  individual  nf  hyper-t  iiene,  now 
altered  to  serpentine,  and  of  pvrite 

The  plaijioclase  forms  a  mosaic  of  well  twinned  grains.  Ihrough  which  are 
distributnl  the  other  coiistitiieiils  in  little  irregular  shaped  grains  of  rounded 
or  siibnnmded  oulliiie  Of  these  the  augite  in  the  most  abundant  With 
the  exception  of  the  alteration  whieli  haso\  crtaken  the  few  hypersthene  grains 

*.-\il:iins,  F,  [),  Kuj.iirt  mi  Ihe  Ociiliii,'viif  ;i  ruriinnuf  ilie  l.anrcnliaii  .\r':i  Ivingtothc 
Norlli  iif  the  island  of  Montreal.  Annual  Report  of  the  Geological  Survey  of  Canada, 
Part  J,  vol.  VIII,  lSi/j,  p   in. 


ED   S■.■^^FACf .   (NAT  .  »4  .    ^.  .' ^  ■ 


■   4  /  WBT 

K 

1,     J 

"^  1 1ll 

i- 

'lUrnV.rrROf'.SAPH   QC    ■  -,  N    section.   (K    3Q    DiAV.-NtCOLS    CRuSSt:;! 


'    I 


ELASTIC   CONSTANTS  OF   ROCKS. 


5« 


the'rock  is  absolutely  fresh.  The  stnicture  is  allotriomorphic,  and  there  is  a 
teiulenev  to  a  panilUl  arrangeinetit  among  the  grains  of  the  darker  con- 
stituents 

.■\  phi>t(iTuier(i.jrai)li  of  a  thin  secliim  of  the  roek  taken  between  erossed 
nieols  in  polarized  light  and  niagnilied  .v)diaineters  is  shown  in  Plate  XII  n 

The  elastie  constants  were  determined  on  a  scpiare  prism  of  the  roek.  and 
as  the  rock  is  very  strong,  the  loading  was  carried  up  to  i.s.'xxj  pounds 
instead  of  <),o<k)  pounds,  as  in  the  other  rocks 

The  figures  obtained  are  set  forth  as  in  the  following  table: 


A  norllwiili-,  Xiw Glasgou;  I'rovince oj (Judnc,  Canada. 

I 


Size. 
Area.. 

i: 


D  . 
C 


I.o;id  lin  pounds). 


ooo 
,000 

CXX) 
tXX) 

000 
000 
,000 
,000 

,0(X> 

,000 
,000 
,ocm 
,000 
,000 
,000 


SI 

101 

I  S7 

264 
31** 
373 
3J-H 
^7^ 
J -'7 
'73 
llf> 
5» 
3 

.99    ■    .99 

981 
1 1 ,9M).(MK) 

.262 
8,368,000 
4,750,000 


I.4ttitntudinal 
coinprfssinn  Lateral 

Iniulliplv  exlinsiiin 

readiiiKs  by  4   .    (millionlhs). 
,  fori.ullitmths). 


81 


^14 
.'60 

j56 

■7') 
'3.'i 
00 

44 
o 


The  averages  of  the  values  found  are  as  follows ; 

£=11,960,000;        -7  =  0.262;        D=  8,368,cxx);        t"=  4,750,000. 

The  stress-strain  car\cs  of  the  rock  arc  shown  in  figure  20,  in  which  I 
represents  longitudinal  compression  and  II  lateral  extension 


5i 


AM  iNvi;sTi(;.\ri<>N'  into  tiii; 


icssicxiTi:, 


'MINT    J'il!N> 


i\.    I'KilVIXCi; 


i|.-    i)ri:ilICC.    CANADA 


•U     : 


This  is  a  ratluTOKirsi'  -raimd  rssoxit.'  frmn  a  qiiarrvcii  the  sln,K.  ,,f  Mnmt 
John..,,,  vvhich  i>  a  tvpu-al  InilU'  arisin,-  In,,,,  the  I'aU-ozoic  ,.la,n  In  ihc- 
s.mth  of  the  citv  of  Montreal  an.i  f..r,iii,ii;  one  of   the    Monlere-,an    H.lls 
The  rook  is  massive  an.l  nniforn,  in  eharaeter  and  .la,k  ^rav  „■  eolor,  and 
is  extensively  used  as  a  building'  stone  and  also  for  nionnnients 

The  iron  ,n  iK-nesia  eonMilnenls  are  represent.d  l.va  violet  an-ite.a  deep 
brown  hornblende,  and  a  biotite  also  verv  (U  ep  bmvvn  in  eolor.the  hrst  n>en 
tioned   beinu  the  n„.st   abundant  an.l  all   three  bein.;  fre.iuentlv  ,ut„nately 
inter-rown      The  liulU  eolored  e.mstitnenls  are  pIa',doelas,'  and   nephehne. 
the  former  btinu  n.ore  abundant  than  the  latl.r.  uhieh  often  oe.urs  as.neh, 
sions  in  the  feldspar      Mllmni^'h   p..|>-MillKlie  twinuin-  is  Ire.p.enth  seen 
in  ,he  feldspar,  a  eonsi.lerable  pioporlion  of  i,  i>  uutwinne.l      A    separat,..,, 
bv    Thonlefssoh,f:on,  h.wever.  .hou>lliat   the    fel.lspar   is   all    plas.oelase 
there   lei,,),'    ""   orthoelase    in  the  roek       Magnetite    in    the    forn,    ol    s.uall 
er.iusan.lapatit.   in  rather  larue.well  delin.  ,1  ervstalsare  present  '"n"'s.d- 
erable  u,nount  asaeees-orv  enuslituents       Tne  roek   is  perfeetlv  Iresh        I  he 
eonstituentsof  tin.  rork,  and  >n,,re  e-peeiallv  the  fel.lspar,  have  a  tendeney 
.A.l;a,i^,    I-     II       11-     M-i't,i,i.u,     Ihll..     .1     l.-:n,:,.l,an      IVI .oi;,.,,l,icMl     Province. 
JounMl.!(<V.>l..irv,  Apill   Miv.  1  CM 


ni.ASTIC    CONSTANTS   OF    ROCKS 


53 


'     No. . 

Size 
I     Afea 

E... 


Eisexik,  Mount  John.um.  Province  oj  Quebec,  Canada 


a  a 

975    V)l     .in  .9'»2  975 


«92  .9025   ■  .9H25   971    1  007 


.966 


.966 


9.580.000 
6.(40.000 


3,781.000 


9.SIIO,000 
.266} 

6,840.000 
3,781,000 


.966 

•ifim.ooo 

2663 
6,840,000 
3  781,000 


886 
9,56.5,000 

2363 
6,060,000 
3.860.000 


978 

10.430.000 

2563 


7.170.000 
4,160.000 


LONGITUDINAI.  COMPRESSION— Ml'LTlILV    REAHlNCiS    BY    4    FO»    M1I.I.IONTBS 


Load  (in  pounds). 


000    , 
OOCI.  . 

,000. 
000,  . 

CXIO.  . 
,(X)0.  . 

,000.  . 
,000   . 

OCX}. 

,000 
000 

OCX) 
,OCXl. 

.000 

(.XX> 
,CXXJ 

,cxx>. 


0 

-  I 

2'; 

OT 

()0 

M 

i)."; 

ICX) 

1,11 

'.Vi 

ifj.S 

\<,n 

20Ci 

200 

2,?K 

240 

270 

270 

2ib 

2.1.S 

100 

2<«) 

l6<J 

17" 

',1,S 

l.v'i 

1(K> 

IllO 

68 

'>.s 

,10 

.(O 

—  1 

-4 

-4 

(>.\ 
100 

1  '•>•> 

U)(> 
2.t'> 
2flfi 
-V(3 
JIJO 
I'l.S 
1.12 

ux> 
6f) 
31 

-.S 


I.ATKRAI.    ICXTKNSION— MlLLlONTHS. 


O 

,1o 

6(> 
ICK) 
140 
l.SO 
21.S 
2fl() 
2'l.5 
2f)0 
220 

140 

no 

70 

2S 

-5 


No... 
Size 


a 
.975 


h 

.9825 


Loud  tin  pounds). 


,IHK» 
.IK  10  . 


,tMKi. 
,000. 


r,(MK> . 


(KXI. 
,tKX». 


(MM). 
000. 


[.000. 

l.oou 


0 

0 

27 

25 

.vs 

4.S 

!(2 

70 

no 

95 

i.tfc 

1.10 

i()i 

I. so 

:HH 

1X0 

22s 

220 

IQ.S 

l.So 

■72 

I.S.'i 

146 

i,?5 

118 

100 

c)0 

75 

4') 

45 

y> 

20 

0 

5 

o 

28 
50 

<*o 

115 
1,50 

l8o 
210 

245 

210 

ISO 
I. so 

115 

<)0 

50 


e 

.971 


195 


54 


AN   INVESTIGATION    INTO  THE 


toassunu-  a  more  lath-shapcd  devi-lopnicnt  than  in  the  case  of  the  granites. 
Tlie  laths  nniniiigas  they  (In  in  all  ilireeticms  thrcush  the  roek,  iimbahly  have  a 
tendency  to  l)in<i  the  rock  nuire  lirinly  loijelher  than  when  the  feldspar  has 
a  more  eqni  dimensional  development,  as  in  the  gra:  i'es.  The  rock  has  a 
hvpidioniorpliie  stnuture,  and.  like  the  granites  desi  :,ed  in  this  paper,  is 
perfectly  massive 

.\  color  pr(K-ess  photo),'rai)h  of  a  polished  snrface  of  this  rock  is  shown  in 
Plate  XllI.N.anila  plioloinierof;raph  of  a  thin  secti'm  laken  between  crossed 
nieolsin  |,ohiri/e<l  liwht  and  maRnilied.vxlianiitersis  toheseen  in  PlateXHI  B. 
Three  square  prisms  of  the  rock  were  used,  and  live  determinations  of  verti- 
cal compression  with  three  of  lateral  extension  were  made.  The  results  arc 
given  in  the  table  on  pa;;e  ,s,? 

The  averages  of  the  results  ohtiiincf)  .in  .is  follows: 

/•:=-  9.74f>.ix>;  '7=^  ()  j.sS.^;  /'  (.,7,s<'.o<K);  t"  =-- 3,873,600. 
Then  Milts  oblaiiud  for  the  Ihn  .  nu  ;iMin  nientson  prism  d  were  practically 
identical  Tlu-  li;;iires  obtaintd  for  in.  ciinipni-' ibilit  v  of  c  are  little  higher 
and  those  for  h  are  consiileralilv  low<  r  flu  .liiTtren.-i  between  the  highest 
and  the  lowest  values  obtained  for  P  anioinils  to  11  lo.ooo  pounds,  but  the 
difTerence.  if  the  results  of  the  single  iiu  as'iri  uu  nt  on  h  be  omitted  from 
consideration,  amounts  to  only  ;,',n,(HK)  ])ounds 

The  stress-strain  curves  plotted  fnun  the  nieasureiiunts  obtained  from  the 
prisin  .;  are  given  in  figure  ji,  and  show  that  the  el.isticitv  of  the  rock  is 
of  a  verv  high  order  In  this  figure  1  npresi  uts  vertical  compression  and 
II  lateral  extension 


l:t      \' 


i  i 


STRAIN 


doo       2^0      eBo 


I'lG.  21  — Mc.u.it  Ji.linsiin  Ks^cxite.    .Stress-strain  curve? 


I'l  •' 


m 


fiLASTIC   CONSTANTS    OH    KOCKS 


55 


r,KKi;\  cAiinKi),  \k\v  c.'.ASc.inv,  i'R(ivi\ti:  hf  i.)ri:iii;c,  ca\ai>a 

Tliis  rook  Idriiis  ;i  hxTfiv  dyke*  iiittiiii;  the  aiiorlliusitc  from  the  locality 
(li'Scribi'd  ahovo  It  is  a  rock  wliu  h  isdarkcr  iiioolnr  iliaii  llic  aiiortlio>itc. 
owiii);  toa  miicli  liij,'lirr  content  of  iron-maijiusia  coiistitiuiits,  out  which,  like 
that  rock,  is  {|iiarried  and  nsed  for  pavinjj  sets 

I'nder  the  ndcroscope  this  rock  is  seen  to  differ  entlrelv  in  structure  from 
'he  other  igneous  rocks  eXiiiiiiiicd  It  is  composed  of  a  cirv  pale  green  auj.;- 
ile,  a  rh  )  nbic  pvrixeiie  of  the  same  color,  and  pl,ii;iocl;-.se,  the  two  former 
minerals  beinj^  present  in  ahont  eipial  amount,  and  the  plajjioclase  tint  forni- 
ini;  more  than  al)onl  one  (piarter  of  the  rock:  ther-  is  also  present  a  small 
amount  of  u  pale  Kreeii  spinel. 

The  rock  is  seen  to  liave  been  crushed  in  a  most  extraordinary  niai:ner  anil 
to  present  a  most  striking  cataclastic  structure  The  plagioelasc  occurs  in 
.groups  of  indis-iduals  which  are  well  twinned,  and  are  freqnentlv  verv  unicli 
bent  and  twisted  Hine  individual  being  bent  through  an  angle  of  ds^  Tlie 
mineral  is  also  filled  with  very  minute  roimded  inclusions,  which  give  to  it  a 
green  color  These  ])lagioelase  grains,  (piile  irregular  in  form,  lie  embedded 
in  a  mass  of  little  irregular  shaped  grains  of  aiigite  and  rhombic  pvroxene 
These  vary  somewhat  in  size  The  two  pyroxenes  are  sometimes  intitnatelv 
intermixed  and  at  other  times  sei)aratL(l  into  groups  of  grains  of  their 
respective  species,  which  are  distinguished  from  one  another  bv  the  ditTerent 
values  of  their  dout)le  refraction  and  by  the  fact  that  one  has  parallel  and 
the  other  inclined  extinction  The  spinel  is  associated  with  this  mimitelv 
granulated  pyroxene 

The  original  structure  of  the  rock  has  been  entireiv  broken  down,  and  it 
now  presents  an  assemblage  of  grains  of  the  minerals  varving  in  size  and 
differing  in  arrangement  from  place  loplace  in  theslide.  The  pyroxenes  arc 
granulated, the  plagioelase  twisted,  and  the  whole  presents  a  perfect  cataclas. 
tic  appearance,  differing  entirely  in  this  respect  from  that  of  the  anorthosite 
just  described.  This  cataclastic  structure  is  combined  in  some  specimens 
of  the  rock  with  a  more  or  less  distinct  parallel  arrangement  of  the  constit- 
uent minerals,  although  this  is  not  very  distinct  in  the  specimen  shown  in 
the  color-process  photograph  of  a  polished  surface  (Plate  XIV  a) 

To  this  irregularity  in  structure  may  be  attributed  the  irregularities  in  the 
elastic  deportment  of  the  rock 

A  photomicrograph  of  a  lli.-  section  of  the  rock  taken  between  crossed 
nicols  in  polarized  light  and  magnified  30  diameters  is  given  in  Plate  XIV  b 

It  is  found  that  satisfactory  measurements  of  t  he  elastic  onnsiants  could  not 
be  made  in  the  case  of  this  rock,  the  same  specimen  giving  a  great  variation 

*Adams  K   D.     Op.  cit.,  p.  121. 


L 


,N   INVKSTir.ATION    INTO  THE 


,,r  variation  i-tl.o„t,l,..nc.,lvNUh.ht"  ,„,,ui,.,u.l,  .1  .s -v-t 

Uie  follovviiiK  l;>W'^' 


li  L 


I,,i..il     in  i."UmU 


I,1«KI 

4.<i>"' 
5,(x«> 
(»,(i*»' 

>  (  M  K  I 


5" 

I  vS 
I  do 
l.|0 

>4i> 
I  lo 


O 

I  t 

-'*! 

47 
S't 
7'> 
'U 

I  :>) 


L.tirul  .-xK-n^i""      1 
imilUitnlli-ii  ! 


s.t 


,s.s 

,!.S 


hi 

4S 
,\.S 
-\S 
I.S 


!      »' 


r*s' 


,,,:,.,,.„..  •on  rin.l  it.  tl..'..tlH'-  '-   V«M«"'      '" 
As  will  IH.  ..en.  /Mnnn.-.as.  '•     ■ ;;  „„  ,..,„u,,„-  ,1k   nu.i- 

„n.nu.n.  of  l>r,-,m  /■  ar.  ..vc,..  |u„!  ^^  ^    ^^    ^^^^,_^^^    ,on,iu,.linal 

o,nn..a:>.n.lv    1ml.    Lv^u-n^.s        "'";_;;;.,.„,.,,„  ,„„aUv  ,o.,.U-urve. 

„    ,'.,„iu.   probable   llKU  both  arc   .orrcU 


KI.ASTIC   CONSTANTS  oK   koCKS 


S7 


In  tin-  table  RivitiR  a  siiimiiary  i>f  results  (scf  page  60),  tin-  values  (;iveii 
fcir  this  r(K-k  repres<-iil  the  tman  of  llusi-  IukIiIv  diverijeiit  readings  ami 
sllimld  be  useil  <>i)ly  in  the  liRht  of  the  explaiiatinii  1,'ivcii  above. 


1000 


40 


i'CX} 


no 


so         im        ISO 

S  TKJIIN 

Ku;    -'-'      ("ptirii  ('i.ililirii,  New  CiliisKow.      Stress    train  iiirvrs. 

UUIVINIC  l>IAllSSi;.   NKAK   Slimt  k\.   I'RUVIN-Ci;  UK  ONTARIO,  CANADA 

This  is  a  verv  tvpiial  frish  olivine  diabase,  which  occurs  in  the  form  of  a 
larKecHke,  ciittinj;roeksof  HuronianaKe  jiist  northwest  of  the  Murray  Mine 
near  Sndbiirv  It  is  one  of  a  number  of  similar  diabase  dyk»s,  which 
occur  in  this  district  of  yre^it  nickel  bearing;  ),',d)bro  iiitriisions  It  is  rather 
coarse  in  jjiain  for  a  diabase,  but  nevertheless  much  liner  in  jjrain  than  any  of 
the  granites  described  in  this  paper,  except  that  from  Westerly.  Rhode 
Island,  these  two  rocks  beiuR  approximately  e(|iial  in  coarseness  of  Krain, 
iilthonsh  dilTerini;  entirelv  in  structure  The  rock  is  composetl  of  violet 
brown  au);ite,  pale  j,'rteu  olivini',  colorless  i)laj,'ioclase,  and  opa<iue  black  iron 
ore  There  is  also  a  verv  small  amount  of  accessory  biolile,  a  few  luiiuitc 
acicular  crvstals  of  apatite,  and  an  occasional  minute  j,'rain  of  pyritc  The 
au^itc  presents  the  usual  microscopical  cliaracttrs  of  this  species,  and  is 
very  fresh,  scarcely  a  trace  of  decomposition  being  anywhere  discernible 
in  it  The  olivine,  which  crystallized  before  the  aiigite,  and  therefore  often 
occurs  as  inclusions  in  it,  while  for  the  most  part  fresh,  is  in  many  places 
partially  altered  to  a  deip  green  serpentine  It  is  nuich  less  abundant 
than  the  aiigite  The  plagiodase  occurs  in  the  usual  sharj),  well  defmed, 
lath  like  form,  always  showing  polysynthetic  twinning  according  to  the 
albite  law,  which  in  llu- same  individual  is  often  combined  with  twinning 
according  to  tin-  pericline  or  Carlsbad  law  It  is  fresh  and  brilliantly  polar- 
izing The  iron  ore,  wiiich  is  black  and  opatpie,  is  abundant,  occurring  in 
well  defined  more  or  less  angular  grains 

The  rock  is  perfectly   massive   and  possesses  a  typical  "ophitic"  or  "dia- 
base"   structure,    the    plagioclasc   having    the   form   of    well-defined    laths 


m 


i?: 

f 


MHta 


!: 

hit 


58 


AN   INVESTIGATION  INTO  THE 


Z  ^."tmi  »™  ..«!  '■<  IK-  «™M  to  „.c.,„  „ri„n,  „f  .ho  ™k  to  fr.,,,, 

•'--;";^^:^r::*  ;;n';:;=«:r .... ...» -;- 

Plate  KV  A,  an.l  a  photo.nicn.Kraph  ..f  a  thin  s.ctu.n  of  Uk- rock  tak.  n  u,  orcl, 
n.rv  li.'hl  and  n.aKnif.ed  27  diameters  is  seen  in  Plate  X\  b 

L  r  t  s    p,eces  were  used  in  determining  the  elastic  constants  of  the  ro  k 
V,       ;     tund  coUnnns  and  one  nearlv  s.,uare  prisn,      They  a-  ^estgna    d 
.     ,    b   c  and  U      The  three  round  colunms  were  cut  out  of  a  bh.k  of    he 
diabas;  bv   nel  o    an  annular  diamond  drill.     For  these  we  are  indebted 
)r   iTLn  Waller  Page,  of  the  Agricultural  Dcpart.nent  at  Wash.ngton 
T.  frntrements  werJ  made  on  each  of  these  in  planes  at  ^fj  -f  ^  - 
,ne  another  m  each  case,  while  four  measurements  were  made  on  the  pnsm 
;;    u:!ngtopai-.f  faces      In  this  way  ten  sets  of  measurements  were  made 
for  the  elastic  constants  of  this  diabase 

The  values  obtained  are  given  in  the  following  tables : 

Olivine  Diabase,  Sudhury,  Onlario.  Canada. 


No.. 
Size 
Area 


d 

1.(11)0  ■    .864 


A- 

l.(MJ 


d 

1.00 


d 

1.00 


864 
£  ..T. .  .      U.ISO.OOO 

'd       1        9,810,000 

C     .....'         5.170,000 


.864 


U,3JO,000 

28S 

10,340,000 

5, 200,000 


.864 

13,450,000 
287 
I     10,500,000 
!      5,230,000 


.864 

1 2,860,000 

.279 

9,655,000 

5,020,000 


---  11     Lateral  extension 

Lonnilurtinal  compression  (multiply  readings  by  4  tor  millionth^.        1| (^ijonths). 


Load  (in 
pounds). 

I,OtX>    . 

2,000 

,^,000. 

4, (XX) 

,S,oo" 

6,(XX)- 

7,000 

H.ooo. 

«),(XX>. 
7,<MH) 


J,(XX> 

I, coo 


Side 
U. 


Side 


Side 


Side 


25 
50 
7.S 
102 

i-'7 
■  .S,i 

220 
19(3 

',S7 
1  V> 


o 
25 
51 
7'> 
10  ( 

130 
155 

i«7 

2>7 

I')0 

'.s7 

1  U 

ins 

.So 

.14 
2- 

i 


25 
52 
.So 

i"5 

i.Vi 

>5J 

IMJ 

ii5 

i«5 

■  55 

1  U 

li'.i 

So 

.V> 

-'5 

o 


26 
5» 
»5 
no 
140 
169 
SOS 
^iS 
200 
1  7,s 

>  ts 

I  10 
so 
SI 


Side  ' 

Side  , 

Side  1 
V. 

0 

0 

0 

25 
.50 

75 
100 

50 

75 
100 

25 
49 

74 
98 

124 

148 
17.? 

■25 

1,-0 
i-,o 

124 
146 

16K 

200 

I9H 

1'I4 

l(iK 
147   1 
12.S  ! 
99 

7.S 
5" 

o  ! 


3^ 


jV.CHOO-t-^H   Of   TMirj   SECT  ON,   U    2!    DAV.-O'-OiNiU-     iGhTI 
.■i  UINF     IrARASE,    SIID3URV,    CANADA- 


5:     '. 


\  I 


I! 


ELASTIC  CONSTANTS  OF  ROCKS. 
Olivine  Diabase,  Sudbury,  Province  of  Ontario,  CoBoda  -Continued. 


59 


:    No 

a 

1          " 

h 

6  ' 

c 

c 





1     Siic 

.981 

.981 

983 

983 

.>83 

.983 

Area  ... 

.756 

736 

1           .738 

i          .738 

758 

.758 

E 

13,2,'iO.OOO 

1.1.780.  OOU 

'     14,020,000 

,    14,320,000 

14,020,000 

14,320,000 

V 

286.5 

281 

291 

.277 

.291 

283 

D 

c  ..... . 

1 

I0.J40,()0() 
5,160,{XX) 

10,460,000 

5,.18O,00O 

11.  170,000 

10,720,000 
1     3.620.000 

11,170,000 
5,430,000 

11,000.000 

3,430,000 

5,380,000 

LuNOITUUINA 

L  CoMPKEsaioN  —Multiply 

Readings  by 

4    FUR    MiLLIONTHS. 

Load  (in 

Side 

Side 

Side 

Side 

Side 

Side 

oounds). 
I.OOO.  . 

U. 

''• 

U. 

P. 

U. 
0 

P. 

0 

0 

0 

! 

0 

2,ooo. 

.10 

.10 

,?o 

!                2.S 

30 

,1" 

3,ooo   . 

60 

60 

60 

!       s-"* 

60 

6n 

4,o<io 

QO 

90 

go 

'            9.S 

90 

8^ 

5,ooo.  . 

I2S 

I  20 

>'5 

1 10 

120 

'I.S 

6,000 

I5.S 

i.SO 

>4.'> 

140 

'.SO 

'4.S 

7,000.  . 

185 

180 

>7.S 

170 

180 

'75 

8,000.  . 

22,S 

215 

210 

200 

210 

^05 

9,000   . 

2. SO 

240 

2.1  .S 

2. 30 

23.S 

230 

8,000  . 

220 

210 

2  m 

2(X) 

210 

205 

7,000.  . 

190 

i«.S 

170 

■7S 

I. So 

'75 

6,000 

16.S 

i.S.S 

14.S 

140 

IS.. 

'45 

5.000. 

1,10 

12.S 

IIS 

",S 

120 

"5 

4,000 

105 

100 

8.S 

o.s 

90 

85 

3,0(X> 

-^ 

60 

.s.s 

.s.s 

do 

60 

2,(K)<»     . 

4.") 

^.s 

3" 

^5 

30 

3" 

1,000    . 

i,S 

0 

0 

0 

0 

" 

Lateral 

Extension  — 

MaLIONTHS. 

No ! 

a 

a 

ft 

983 

b 

c 

983 

c 

Siie 

.981 

.981 

983 

.983 

Load  (in    ! 

Side 

Side 

Side 

Side 

Side 

Side 

pounds),    j 

U. 

P 

V. 

P. 

I.'. 

P. 

1,000.  .1 

0 

0 

0 

0 

0 

0 

2,000.  .1 

78 

28 

28 

25 

21 

27 

3,000.  . 

.'54 

.SI 

.S4 

40 

49 

53 

4,o<w).  . 

8.? 

78         1 

82 

73 

78 

79 

,S,fxx>   . 

1 1  I 

1 0.1 

1 10 

100 

K'S 

107 

6,000   .1 

140 

l.^o        1 

I. IS 

I  22 

131 

'.V 

!     7,o(X).. 

169 

i.sA    : 

l(,4 

149 

1()<> 

'S4 

1      S,<xx>    . 

1 98 

1 8,? 

lifi 

I  72 

185 

'83 

9,fXjo 

2^,S           1 

210        1 

-'I.S 

21 K1 

2IS 

205 

H,ooo 

200 

I.'*';      1 

1<I2 

171 

"),S 

180 

7,000   . 

'7- 

1  ss 

1  7*> 

1  S'l 

170 

166 

6.(K^( 

1  U 

1  i=i 

1  1(1 

I  25 

1  IS 

'.V> 

3.<MH1 

I  li 

1  i<i 

1  1.^ 

IiX) 

1  1  s 

1 10 

4,000 

^.S 

7.S 

,^S 

7S 

8.S 

So 

.■^,000 .  . 

5-        i 

5+ 

.S6 

so 

S.S 

55 

2,000  .1 

22 

2() 

30 

2S 

25 

26 

1 ,000        : 

0       i 

1 

0 

0 

0 

0 

0 

i  1 


\ 


■  t 


6o 


AN    INVRSTIC.ATION    INTO    THE 


As  will  he  ...n.  the  vahus  nbtaine.l  for  /;  in  this  roek  are  -:"-«;-'';;;>  ^f^^ 
„;,„  those  vuMe-l  hv  anv  other  rock  of  the  senes  exanune.l  It.  the  s.x 
;;.Wn,  nu.asurc:.nents  earrie.l  out  on  the  first  three  M^---;  ^ 
,i,Te  eneebeuveenthe  highest  an.l  lowest  vah.es  for  P  a.nounte,  t  S. V.ooo 
'  ,„.ls,  while  o„  the  four  uu.asure,neu,s  nuule  on  speeunen  ./  tlur.  .s  a 
r  iiher  L'reiter  .liffereuee  amounting  to     I'^.iioo  pounds 

Th^  a^nisllf  the  .leternnnations  uK.le  on  each  of  these  colun.ns  are  as 

follows:  _. 


/.    

I  ■  ■     

d 

Average 


E 


M,  5 15.000  io,4<K>,ooo 
14.170,000  '  10,1)45.000 
I  1  \-cifyoo  '.  ii,oS.s,ooo 
•     017,750     io,07(",ooo 

13,763,1X7  j  10,626,500 


o.2!<vS  i  5,270,000 
0.2S40  \  5,525.«'0  I 
o  2S70  j  c,,v>5.oo<>  1 
0.2H12  I  5.1S5.0OO 

0.2840  i  5,36,1.750 


The  stress-Strain  curves  siven  bv  a  specinien  this  rock  are  shown  in  fignre 
. ,  As^n,:  ;;;«  from  these  curves,  in  its  approach  to  perfect  elasticity  the 
rock  isconipural)le  to  plate  sjlass. 


80  120  '*" 


.I-ir,. 


-SiuUmiy  Diab;ise.     Stress  strain  curves. 


SANUSTONI!,  ei.i:Vi:i.ANl>.  OIll«l.   t'NITKD  STATES. 

This  is  a  fine  an  1  even  ,raine,l  vellowish  san-lstone  used  verv  extensivel  v  for 
hui      ,.'   purp  .ses       l-he  hed.lin,  is  marked  by  a  sh.ht  varution  in  colo 
b     1  T^e  It    .eds      The  prism  of  the  rock  used  in  determining  its  ekst.c 
on       US  was  cut  from  a  siuK-e  bed  of  uniform  character  and  color,  and  was 
taken  in  the  plane  of  the  beddin,      A  color-process  photograph  of  a  smooth 
surface  of  the  rock  is  shown  in  I'late  X\'I  a  .  ...  .  . 

Uuer  the  microscope  it  is  seen  to  be  a  typical  highlv  feldspathic  sandstone. 
The  constituent  minerals  arc  present  in  grains  which  arc.  approximately 


V'   ^'      WAPM    OF   TMtN    SFCTiON,    ',  X    ;;  ,'    D' AM  -  C'i  0' N  AK  >     I    i 


-.iV/  V-*k'i^'«?^-  .-.■«•- 


".tarvMi^ttwaiaQrrh? 


'..^jJf^Latr 


ELASTIC   CONSTAN'S  OF    ROCKS 


61 


uniform  in  size  and  of  rmlfly  rounded  or  suhaiiRular  outline  The  <|uarlz 
>;rains  are  clear  and  fresh;  the  feldspar  indiviiliials.  which  are  abtnulant,  on  the 
other  hand,  are  for  the  most  part  in  an  advanced  sta^eof  alteration,  hi  inij 
alvvavs  turbid  and  in  most  easeS(|uileopa(pie.  from  the  presence  of  alleraliiui 
products  .Some  few  jjrains  of  comparali\  elv  tmaltericl  planioclase  are.  how 
ever,  present,  and  scaltered  IhrouKh  the  rock  there  is  a  consideral)le  amount 
of  hydrated  oxide  of  iron,  which  often  lies  between  the  Rraiiis,  furmiiiK  a 
cement  The  rock,  however,  also  contains  a  not  inconsiderable  .imount  of 
calcite.  which  causes  it  to  effervesce  slishtlv  when  treated  with  dilute  hvdro- 
chloricaeid.  and  which  is  also  seen  '  ■  lie  between  the  clastic  grains  also  form- 
ing a  cement,  often  in  the  form  ol  individuals  of  a  size  comparal)le  to  those 
of  the  other  minerals 

The  rock,  however,  is  not  a  ervstalline  rock,  but  a  typical  clastic  one  There 
is  not  a  continuous  crystalline  web  or  mosaic.  Init  a  mass  of  roundedorsub 
ansular  strains  which  are  in  part  cemented  together  as  above  described,  but  in 
part  are  separated  by  minute  open  spaces.  It  is  to  be  expected,  therefore,  that 
the  rock  will  show  serious  defects  in  elasticity,  as  proves  to  be  the  case 
when  attempt  is  made  to  determine  its  elastic  constants  A  pholomicroj;raph 
of  the  rock  taken  in  ordinary  light  and  multiplied  27  diameters  is  shown  in 
Plate  XVI  n 

A  square  prism  of  the  rock  was  employed,  and  it  was  f(mnd  to  be  dangerous 
to  submit  it  to  a  load  of  over  4.(kx)  pounds,  the  crushing  weight  of  the  rock 
being  much  lower  than  that  of  the  other  rocks,  which  are  crystalline  in  texture 

The  figures  obtained  are  given  in  the  following  table: 
Sandstone,  Clenlanii.  Ohio,   Umtfil  Slitles. 
I     Size 


D  . 
C  . 


ill  ponnilsi. 


I,CXX>. 

4,fKN). 
_1.00(J. 
i.OOO. 
1   000. 


i.ooox  1.02s 

1.023 


2,290,000 


.29 

1,816.000 

gSD.OOO 

I,i>li^ituclin;it 

ctiiiipris^inn 

(iiiitllipK 

rf;i(llii^:'-  \>\  4 

for    iiiiiliiiinhsi. 


I. Si 

2S,S 

4  it. 


1.000 

— 

I.aUT.il 
iiilliotith^i. 


'73 


63 


AN    INVESTIGATION    INTO    TH'i 


The  stress-strain  curves  are  sMdwh  in  figure  .'4 

As  will  be  seen,  the  rock  displavs  a  marked  hysteresis  and  is  nut  there 
fore  an  ideal  material  fur  the  ajiphcation  of  tliis  method  of  deterinininKConi- 
pressibihty 

The  rcsidts  obtained  are  as  follows  : 


E 


2,2()ti,i>*  Hi; 


"  =  0  Jij; 


n 


,8l().'Kx;; 


8S.S,<)iXJ. 


§  2000 
•J   1000 


ao        no       mo       too      2*o      lao      320 

5  TRAIN 
Fio,  24. — Sandstone.     Stress-strain  curves. 


400 




440 


% 


THE  ELASTIC  CONSTANTS  OP  GLASS. 

As  in  geophysical  speculations,  the  earth  in  aspect  to  its  rigiditv  and  com- 
pressibilitv  is  often  compared  to  a  globe  of  glass,  it  seemed  advisai.le  to  deter- 
mine as  accurately  as  possible  the  elasticconstantsof  glass,  for  the  purp'ise  of 
comparing  them  with  the  results  obtained  in  the  case  of  the  various  rocks 
considered  in  this  paper,  employing  the  >-,ime  methods  and  carrying  out  the 
work  underexactly  the  same  conditions.  This  material  lends  itself  excellently 
to  this  method  of  measuring  these  consta'its,  provided  the  glass  is  free  from 
all  irregularities  in  its  substance  and  is  isotropic  in  character  he  first  diffi- 
culty experienced  was  that  of  obtaining  such  a  glass.  At  the  outset  it  was 
thought  that  thick  glass  rods  such  as  arc  used  for  various  purposes  in  the 
chemical  and  physical  lab  iratorv  might  be  employed,  but  although  several 
lots  of  the  purest  variety  of  this  material  were  procured,  the  gK.ss  constituting 
it  was  found  in  all  cases  to  contain  minute  air  bubbles,  and  when  examined 
between  crossed  nicols  in  polarized  light,  -allowed  brilliant  colors — red, 
yellow,  and  blue.  This  indicated  a  state  of  marked  tension  in  the  glass,  evi- 
dently due  to  the  rod  having  been  drawn  when  the  giass  was  in  a  viscous  state, 
which  was  also  shown  by  the  circular  arrangement  of  the  little  bubbles  in  the 
rod,  following  the  direction  of  its  surface  .Short  lengths  of  this  rod,  moreover, 
when  tested  in  compression,  so  soon  as  the  maximur.i  load  had  been  exceeded, 
instead  of  splitting  from  top  to  bottom,  broke  as  if  composed  of  a  series  of 
rudely  concentric  shells  All  attempts  on  the  part  of  the  various  glass  makers 
to  whom  this  glass  wa  submitted  for  a  thorough  annealing,  failed  to  remove 
or  in  fact  to  redu'     to  any  considerable  extent  this  anisotropic  condition. 


ik 


ELASTIC   CONSTANTS  oK    KoCKS 


63 


The  fiKurisobtaiiU'd  fmiii  one  of  llusc  glass  ro«ls  approximately  an  inch  in 
diameter  are  giveii  in  the  foUowins  Uble: 

Gttiis  Koti. 


Arc*.. 
E  ... 


D 
C 


I.oiid  (in  p^mnds). 


000 
OCX) 

,000  , 
,ocx>  . 

.CXJO  . 
,rK)0  . 
,IKH» 
,0<H>  . 

000 

000  . 
,(XX>  . 

000  . 
,CXX)  . 

OC»  . 

000  . 

,000  . 

,000  . 


774 

H.075,000 

2 

.t,j6l,oaa 

l.nni[itmlitl.il 
inmpriMsioii 

(muUit)ly 
nMilinu**  liy  4 
for  mjllionths). 

o 

.S.S 

<I,S 
U.S 
-'(K> 
2  VI 

.'S<> 

.ISO 
.V'.-i 

-'".1 
l^Hl 
I  IS 

,S 


l.atrrni 
rxlrnsiim 
(inillionths). 


W 
hi 
<)5 
I.!.( 
I. S.S 


I  Si 
US 
1(X) 

.vs 


That  the  tension  in  this  glass  senonsly  affected  the  results  obtained— as 
might  t.e  e.xpected  -i.s  clearly  seen  in  the  value  for  U  being  much  too  low,  as 
will  be  shown  latei'. 


9000 


160       zoo 

STRAIN 


'•;g.  25.     Glass  RihI.     Stress-strain  curves. 
The  stress-strain  curves  plotted  from  these  values  are  shown  in  figure  25. 
As  will  be  seen,  the  material  »xhibits  a  distinct  hysteresis. 


64 


AN    INVKSTIOATION    INTil   TIIK 


Aftir  a  pn limited  search  for  ivitropic  j;lass  in  niassfs  of  Miflicicnt  size  to 
ini' isiirt'  the  tiastic  cnnstants,  it  was  fiiuml  that  platv  i;lass  answert'd  the 
ref|iiiriiiifiils  A  piece  iif  mu-  inch  plate  glass  made  in  (Ireat  llrilain  was 
accurditiijlv  seciirwl  and  was  cut  into  strips  an  inch  wide,  and  these' again  into 
tline  inili  lengths  The  sipiare  prisms  thus  produced  were  then  pro|K  rl\  faced 
and  polisluil  Till'  u'^'ss  was  found  to  he  al)solutelv  free  from  all  Haws  aiul 
iuipuriliesand  when  examiiud  l)elween  crossed  nicols  tin-  prisms,  although  an 
inch  thick,  showed  in  one  direclion  at  right  angles  to  vertical  axis  ahsolute 
hiackiu'ss  lhron;;liout  a  coiupleii'  revolution,  while  in  the  other  direction  at 
right  angles  to  this  there  was  during  a  revohilion  an  alternation  of  blackness 
with  a  pale  grayish  illumination  This  change  w.is  so  -.light  that,  considering 
the  thickness  of  the  glass  mil  the  sensitiveness  of  the  lest,  the  material  may 


<a 

^  rroo 

o 

«J  sooo 


/ 

ffl^ 

y^ 

/; 

r 

^ 

/ 

IX 

ftO  U^O  im  200  240 

,<;  TRAIN 

Vu'..  2(i      I'late  Ohiss,     Stress-strain  curves. 


It 

PI 


be  considered  to  be  praclicj'lv  free  from  internal  tension  and  to  be  isotropic 
in  character 

In  order  to  get  a  good  average  .iiid  to  eliminate  chance  errors  as  far  as  possi- 
ble, seven  of  Uiose  prisms  were  taken,  and  two  complete  sets  of  determinations 
were  made  (m  each  of  them,  using  in  every  case  ilifleren*  pairs  of  faces  Four- 
teen determinations  were  thus  made  of  each  of  the  elastic  constants  The 
tigureso'.)!  lined  are  set  forth  in  the  table  on  page  6s. 

In  this  t,il)k  a  complete  series  of  values  obtained  from  each  specimen  are 
given  in  double  rows  When  the  ;:ve,agi'  of  all  these  results  is  taken,  the 
values  obtained  for  the  sr\er  '  constaats  of  plate  glass  are  as  follows: 

/?=  io,,soo.rxx);         "  =  0227,^;         i>  =  6,448,000;         C=4, 290,000 

The  stress-strain  curves  given  by  one  of  the  prisms  is  shown  in  figure  26. 
In  this  figure  I  represents  longitudinal  compression  and  II  lateral  extension. 


Kl.ASTIC    CONSTANTS    Of    RDCKS 


«S 


h'UtU-  (ilao. 


Si/i-     . 

*ms\ .  I  u ' 

Ana 

1    IHIS7 

K 

til    \Mt  <KHI 
Itl  S'ill  IMHI 

•  . .    ■ 

22»l 
,2rt 

/>    . 

fiMo.onit 
1,  tm.ww 

C 

1  jiD.mio 

4,110,111111 

'I'!} 


fi.SNit.iHMI 


'tNl  >  I    Ml  tS       I 


■♦•SO. 


4.1'*il,tHM) 


III,  mtiiuMi 


»(.  »Sl>,»W 


-l.iltl  'KM) 
4..Ml),t«NI 


1121  >'    •»'>SS     I    (I. 

I    11 ; 


Ii(.4Mi.(M>n 
III  'MO  iHtti 


I    IMIJS     I    n.MV  ,'1'*4 

(i.M  I   nl<.       ' 


in  iso.MMi 
10, 2*11. 'xm 


22't 
.2i^ 


ti,4tll.(MM) 


4,22l).IMH» 

I,  tin, (MM) 


f.,I40,iMKI 


4.  tMMNNl 


I^^NOl^^'rl^^JAt.  v  ovmBssiDN^MuLriftv  Khaihnus  mv  ♦  rtm  MiLLioNrHH. 


IahuI  un 

s,,u. 

SUIv 

S1.I. 

^I4le 

Si-lr 

Si-If 

Siilr 

Siiir 

Siile 

Stit» 

Siilr 

SmIc 

Sidr 

Sul« 

IMlUtKliI 

(.' 

(■ 

/• 

/> 

«' 

f. 

I'. 

;• 

('. 

/• 

C. 

/'. 

U. 

)*, 

I.OfJO 

(1 

c» 

0 

1. 



<i 

0 

1) 

0 

„ 

11  1 

11 

0 

0 

11 

2,Cir)(> 

,v> 

3'> 

-'5 

30 

V> 

30 

3" 

3" 

V> 

3" 

JS 

2S             V* 

U' 

v'HMI 

fK) 

55 

55 

(m 

(Kl 

(K. 

(m 

Im 

(xi 

55 

ss 

SS         (m 

(HI 

4,(¥K1 

IJ<I 

Si 

^5 

<(o 

"K) 

")<> 

1)11 

•(O 

110 

ss 

■s 

S5            Ss 

1)11 

5.<«K. 

1  io 

1  15 

"5 

120 

1  20 

1  20 

1  JO 

1  1  5 

1  15 

1 10 

s 

no  1    IIS 

12s 

(l,(»0*> 

14,^ 

'45 

'45 

145 

1-,.. 

1  SO 

150 

'45 

145 

135  : 

■  15 

14"  i    145 

'  15 

7,ooo 

'7S 

'75 

'75 

'75 

ISll 

fSo 

l>-.l 

175 

'75 

170  ' 

'75 

170    i      ISO 

'75 

«,OtX3 

JIO 

-'"5 

-'"5 

21C1 

210 

J  10 

21>5 

20  s 

Jo  s 

l')5 

JIKI 

i'J5  i    211s 

210 

9,oon 

-'4" 

-'35 

-'.V 

2(1) 

24" 

243 

2  15 

2  vs 

J  IS 

22s 

235 

2  VI       2,1.5 

-']■•> 

8.00C1 

JU» 

-•"5 

-'"  = 

2ni 

210 

211) 

2115 

20  i 

■■'  15 

"(5 

2115 

l<I.S   '    20s 

210 

7,ooo 

iMt) 

I  So 

'75 

ISO 

iSo 

ISO 

■Ho 

i:s 

175 

170 

175 

I'll      17s 

ISO 

6,(>iic> 

I.S« 

1(5 

'45 

15" 

15I' 

'  v5 

1  Vi 

1  IS 

1  15 

1  IS 

I  |i 

I  111          'IS 

ISO 

5.w)i> 

l,!<> 

"5 

"5 

I  .»o 

I  20 

1  20 

1  JO 

1  ■  s 

1  15 

,10 

1 15 

115         IIS 

I  20 

4,ooo 

')<> 

!<5 

1*5 

i)0 

.(11 

1|0 

1(1  > 

<(0 

ss 

SS    ' 

^5 

ss          S,s 

i|o 

3.000 

(Kl 

55 

55 

60 

(.0 

f«l 

(HI 

is 

5S 

(Ml 

"• 

(>0               (H) 

(.0 

2,ilOO 

30 

3" 

25 

3'> 

3" 

3" 

3i> 

3" 

3" 

(O 

3" 

3"          3" 

3" 

I.OOO 

0 

0 

II 

" 

0 

0 

0 

1) 

1) 

11     1 

0 

0            0 

0 

tArUK 

AL    iCxi 

BNSl.    S 

-Mill  1 
l> 

ISTIM. 

0 

I.OOO 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

2,nno 

2  J 

2  2 

21 

22 

") 

22 

211 

Hi 

•11 

1') 

20 

II)   1       21 

2(1 

3.(K1«> 

44 

45 

42 

45 

3S 

4I' 

i'l 

11) 

4" 

4' 

3if   i      42 

42 

5  ^*** 

OS 

()S 

()6 

6S 

(Ml 

1..) 

><>, 

MO 

5'( 

'15 

(.0    ;       (10 

(•2 

S.) 

«() 

8S 

S.) 

Si 

')2 

-1 

So 

Si( 

7'l    '       S<) 

!     **3 

(l.(KX> 

1 1 1 

III 

IO<> 

1 1 1 

im 

"5 

'  ' 

Ills 

10  ■ 

UK) 

UK) 

100    1     100 

1    '"3 

7,ooo 

>ii 

133 

'2') 

'33 

'-•1 

13s 

»^ 

12(1 

I  J  I 

I  22 

I.V> 

122    \      122 

i    '-'- 

8,ooo 

'53 

15<> 

'5' 

'5" 

'4- 

K.o 

'57 

Its 

I  15 

I  1  1 

'55 

145  ;  144 

!  '■♦4 

9,ooo 

'73 

'75 

'72 

'79 

170 

ISO 

17H 

l(,.( 

1(.|( 

Ili.S 

17!) 

Ids 

"'7 

'<>5 

8.000 

'55 

'55 

'52 

'57 

■4'» 

I'M 

159 

l»'l 

1  |'> 

-45 

155 

'47 

•4') 

■47 

7,ooo 

'35 

133 

'30 

'35 

12s 

140 

'35 

121) 

I  2f) 

I2S 

IV> 

125 

'25 

125 

6,oon 

1 15 

1 1 J 

110 

"5 

'03 

I  >5 

100 

llMi 

"'5 

105 

112 

'"5 

'"3 

!  1116 

<>3 

<|o 

'(«> 

C)0 

So 

i)l> 

S,( 

SS 

ss 

H8 

QO 

!<5 

82 

Sq 

4.H.H) 

7'* 

71 

7<i 

70 

hi 

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04 

62 

6j 

62 

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65    1        f)2 

(,Q 

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45 

45 

51) 

41  > 

(2 

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42 

4' 

4' 

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43         42 

49 

2.(KX1 

23 

22 

25 

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20 

20 

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22         22 

2S 

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° 

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0 

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66 


AN    INVKSTK-.ATION    INTO    TIIIC 


jl        .' 


nitmnin.itions  of  the  cul)ic  coniimssihilitx of  ylass, />,liave  hern  iiiaiK'  hy 
otliiT  ohscrx  ITS  usitiK  various  nulliods  Tlu- risults  u"  tosliow  that  dilTcrcnt 
vaiitti.s  (if  k'la^s  vary  coiisidirablv  in  thi'ir  omprissibihty  'I'hcsc  di-tirttii- 
nations  tiiav  hv  tahulatid  as  fiillo\v>;* 

l-lviriit      5,o;.t,(.iH.ln(.,,(7'M"<' il-'   <■   ^  "=-  '^ '"  t  t       '""'■ 

AniMKal     C.iinmcmKlass.    .         (,,;  i,s.ih«i  i  .i"-'»>"-i  M  per  ;i  I  inn-,], lure). 
Aiii:iK:il     Crysl;il  Klass     .  (,,,  u,  (.«>  i  (xhkk.j  ,i>s  per  ;itTin.s|,1,m-i. 

•|-.,j,  ^,li;i;,7i«)  (.(KXKKl.'d  JHT  alinn'-plllTll. 

As  will  bt  seen,  the  tlRures  obtained  for  plate  Rlass  in  the  present  iiiveslis;a- 
tion  lie  a  little  above  the  average  of  the  various  values  here  given,  and       e 
nearlv  those  of  the  highest  value  obtained  bv  Iiveretl 
SUMMARY  OK  RESULTS. 

The  table  on  page  6<)  gives  a  sunnnarv  of  tin-  average  values  obtained 
for  /•:,  ■'.  (■  and  /'  in  f'e  ease  of  all  roeks  examined  in  this  investigation 
With  these  are  placed,  for  purjwises  of  eoniparisou,  the  results  obtained 
for  these  eonstanls  in  the  e.ise  of  wrought  iron,  east  iron  and  glass  In  the 
second  table  .^n  page  69  these  \  alues  are  again  presented,  recalculated  into 

C   (»    S    units 

The  rocks  fall  naturallv  into  three  groups,  dilTering  from  ime  another  in 
eonipressi')ilitv,  but  the  several  members  of  each  group  agreeing  fairly  closely 
among  themselves 

These  thrie  groups  show  a  correspouiling  dilTeretiee  in  composition 

The  first  group  consists  1  >i  the  marl)les  and  limestones  These  have  an  aver- 
age value  for />  of  6,  u.s.ooo  Oneof  these,  however,  the  Ulack  Belgian  marble 
which  is  verv  much  finer  in  grain  than  the  1  it  hers  and  breaks  alm<ist  like  a  piece 
of  glass,  hasa  vervmuchhiglier  v.ilne  for  /'  than  that  possessed  bv  the  other 
niiM<s  which  auMiig  tluuiselves  are  nearlv  identical  If  we  <iniil  this  Helgian 
marlile,  the  average  of  /'  for  the  other  limestones  and  marliles,  is  5,S,s,S,oo<). 

The  second  group  comprises  the  granites  These  again  show  a  close  agree- 
ment of  values  am.mg  the-ii.clves.  e\ce|r.  in  the  case  of  the  Staiistead  granite, 
which  rock,  as  alreadv  mentioned,  shows  a<lefective  elaslicity  The  average 
value  of  /'  for  the  granites  is  4,.V)').ooo 

The  third  group  embraces  the  basic  inlrnsives  (gabbro,  anorthosite,  essexite, 
and  diabase)      These  show  greater  dilTereuees.   but    ha\i-  an  average   value 

for   /)  of   .S,,Sjs The   nepheline   svenile,  although  higher  in  silica  and 

tlurefore  properlv  speaking  an  acid  rock;  in  its  freedom  from  (piartz,  and  its 
richness  in  feldspar  (although  the  feldspar  is  largely  orthoclase  instead  of 
plagioelase),  in  nnneralogieal  composition  belongs  with  these  basic  rocks 
rather  than  with  the  granites  It  alsoapliroaches  the  essexite  most  nearly  in  its 
compressibility 

"Vsrcliviri-lt,  Illnstratiuns  „f  llie  C.  C.  S,  Systt-ni  i.f  I'nitswith  tallies  iif  Physical  Con- 
st.ints,  .Niac.Millui  H  Co.,  n^j:.  pp.  '«>  t"  'H-  The  figures  there  expressed  in  various  units 
have  been  here  recalculated  int(i  Inch -pound  values. 


^^VlVrfri 


u. 


KI.ASTIC   CONSTANTS  OF   ROCKS.  °7 

If  the  nc-pl.cliiu.  syonitf  be  incUuled  with  the  basic  n.cks,  an  averafie  vaU.e 
of /)  is  obtained  (pf  .S,;,()H,iKX) 

This  omits  In.m  o.nsideration  the  sandstone,  it  Ixing  a  rock  of  an  entire! 
.lilTerent  elass  fnm.  the  ,.thers,  an.l  fnrther.nore  one  whieh    shr.ws  so  nineh 
I,vstere,is  th,.l  the  appheation  ..f  this  method  to  it  is  less  sat.slactorv  than 
in  the  case  of  the  other  rocks  of  the  series 

'I'liese  results  inav  he  presented  as  follows ;  .  ,  „ 

(i,^4S.ooo 

Marhlc.  .M.,1  lM„est..nc 4,,.,r,,oo., 

^■■•■'"""       :    .    H,;v>H,<K>o 

ll.isic  intnisivi-s 

The  cause  ..f  the  much  greater  compressibility  of  Rranite  as  cr.mpare.l  w,th 
the  marbles  and  basic  i.Urnsives  is  not  clear,  but  would  seem  to  be  connected 
with  the  presence  of  ,,nar..  The  only  detennination  of  the  cub,c  co.npress- 
ibilitv  of  .p.art..  s.  far  as  can  be  ascertained,  is  one  bv  \o,«t,*  the  value 
obtaine.1  beint;  5,504.  .')o  poun.ls  (.,S7  <  ">"  Rrams  per  sq  cu.  )  Tins  com_ 
nr.ssibilitv  as  will  be  seen,  is  m.ich  greater  than  thai  found  m  the  case  ol 
either  the  liM.estones  or  the  basic  intrusives,  a.ul  while  not  m  itsell  suf- 
fu-ientlvK-reat  toaccount  for  the  hifih  compressibility  of  the  «ra.utes  j^oes  to 
show  that  m  the  .p.nrtz  we  have  a  mhural  which  is  n.ore  con.press.ble  than 
theonlinarv  rock  makinj;  minerals  which  f.,rm  the  chief  constituents  m  the 
rocks  of  the  series  examined  .-,,•.  , 

■Ihe  marbles  and  the  limest.mes  of  the  earths  crust  are  confined  to  Us  most 
superhcial  portion,  resultiu-,;  as  thev  do  from  the  process  of  sednnentatu.n. 
There  is  everv  reason  to  believe,  however,  that  what  we  may  term  the  sub- 
structure of  the  earth's  crust  is  imposed  of  acid  an.l  basic  plutomc  isneous 
rocks  These  make  up  the  lowest  part  of  the  crust  to  which  we  have  access 
and  are  found  comin;;  up  from  the  still  K'reater  depths 

The  cubic  cotnpressibihtv  P  of  the  earth's  crust  must  he  between  the 
values  LMven  above  for  the  granites  and  the  basic  intrusives,  appn-achniR one 
or  .,ther  of  these  values  according  to  the  relative  pn.portion  m  it  oi  one  or 
other  of  these  classes  of  rocks 

If  we  t  ike  .he  average  of  the  values  obtained  from  these  two  classes  of  rocks 
as  r  .resented  bv  the  seven  granites  and  the  five  basic  intrusives  {includnig  the 
nei.helincsvenite)  the  values  obtained  for  Oof  6,.15,V,5'X>.  ,      .      ,, 

This,  as  will  be  seen,  <liffers  but  little  from  the  value  of  /)  obtained  for 
plate  glass  whieh  is  6,448,000 

If  therefore  theearth  's  crust  be  composed  of  granite  an.l  basic  igneous  rocks 
in  approximatelv  equal  proportions,  its  compressibility  will  be  that  ol  glass 
If  it  be  comp..sed  almost  excl.isivelv  of  granite,  the  earth  's  crust  will  be  more 

'^^eT  in  lUeker:  Uxpcrlments    on    SchiMnMty  :.nd  Sluty  Cleava«c,   Uulletin  .4., 
U    S  Gcol   Snrvey,  p.  32. 


6« 


AN   INVESTIGATION   INTO  THE 


t'-    i 


compressible  than  Riass,  and  if  the  basic  rocks  preponderate  very  largely  it 
will  I)f  less  cijinpressibk'  than  this  substaiioe. 

It  is,  however,  in  anv  case  much  more  compressible  than  steel,  which  has 
a  value  for  /)  of  from  2(i.n.)H.i)i>:)  to  37,s47,(«k)  (iH  to  i>)  x    lo",  C  G.  S  ).* 

The  c  'Uipression  to  which  tlie  rocks  were  subjected  in  this  investigation 
ranged  from  6,000  to  17,^4(1  pounds  to  the  square  inch  Most  of  the  rocks, 
however,  were  subjecled  to  a  load  of  from  (),(>oo  to  iS.oim)  jjounds  per  square 
inch.aiil  ihiir  Iv.ilk  compression  was  determined  for  thesf  loarls  as  maxima 
Hiiiher  pressures  could  n.it  be  emijloyed  without  running  the  risk  of  breaking 
the  specimen  and  at  the  same  time  of  destroying  the  measuring  apparatus 
One  apparatus  was  in  fact  so  destroyed 

The  questi,  >ii  aris.s  as  to  whether  under  still  higher  pressures,  if  rupture  could 
be  avoided,  the  ratio  of  load  to  compression  would  be  maintained  Judging 
from  the  deportment  of  much  stronger  substances  such  as  steel,  when 
similarlv  ttsled,  it  is  iuferiiil  tliat  this  ratio  of  bulk  compression  will  remain 
coiistiiut  fur  very  uujch  liiglur  pressures,  or  until  deformation  sets  in  and  the 
rock  begins  to  llow 

With  regar.l  to  the  aceur.icv  of  the  r..sults  obt;iined  by  this  method  as  com- 
pared with  those  obtainable  bvany  method  in  which  cubic  compression  is 
actually  produced  and  measured,  it  mav  be  observed  that  by  fir  the  best 
methodof  this  kind  hithertosuggested  seems  to  be  that  proposed  b>,  Kichards 
and  Stull  t  We  have  endeavored  lo  make  use  of  this  method  in  order  to 
obtain  results  for  purposes  of  comparison  with  those  given  in  the  present  paper 
but  have  not  hitherto  succeeded  in  overcoming  certain  experimental  dilliculties. 
The  exi)erimeutal  errors  in  this  method,  though  appareutiv  small,  still  exist, 
and  in  applying  it  to  rocks,  which  are  much  Kss  compressible  than  the  sub- 
stances examined  bv  Richards  and  Stull,  these  errors  become  proportionately 
more  serious  Moreover,  higher  pressures  than  those  used  in  the  method 
emploved  in  tlu>  pese-it  p,q)er  could  scircelv  be  emploVefl  in  this  direct 
method,  while  dil1icidli/s  de[)fU!leul  on  the  possible  lack  of  absolute  contin 
uitv  in  the  substance- of  the  rock  and  the  danger  of  minute  air  lille<l  spaces 
wouM  probably  present  themselves  in  the  case  of  most  rocks  It  seems  that, 
all  things  being  considered,  the  indirect  method  here  employed  is  probably 
as  accurate  as  anv  direct  method  which  can  be  used  The  attempt  to  apply 
Richards  ,ind  Stull's  method  to  rocks  is  still  being  continued,  however, 
and  it  is  hoped  that  satisfactory  results  may  be  eventually  obtained  by 
its  use 


1^ 


♦Illuslniti..ns  ,,f  till'  C    C.   S    System  ,if  Units,   witli  IVliIcs  of  Physical  Constants 
M:ieMillaii  Sr  Cn  ,  mnj.  |).  (,n. 

tNmv  Mi'thiiil  ijf  I)i'tfrmiriiii;l.'cmipreiisil)ility. 
uf  Wasliinuton,  December,  ii)o,i. 


riil)!islR-il  liy  t  lie  Carnegie  Instituliun 


ELASTIC    CONSTANTS   OF    ROCKS. 


6q 


Elastic  Constants  oj  Rnrk^. 
SuMM   Rv  OP  Results  (AvuRAr.K)   ICxprehsed  rN  Inch  IN>UNn  ITnits. 


Specimen. 


Wrfiimht  iron.. 
Cast  ir<in 


HIack  Ik'lj;ian  luarhle 
Carrara  niarli'       .... 
Vcrniciiil  man  if. 
Tennessee  ntarl)le. 
^tontre:tI  iiinestone  . 

Havenc  granite 

Peterhead  granite    .  .  . 

Lily  Lake  granite 

Westerly  granite        . 
Quincy  granite  ( i )     . 
Quincy  granite  (j) 
Stanstead  granite 


Nepheline  syenite 

New  ("rlasgow  anorthosite 
Mount  Johnson  essexite  . 
New  Glasgow  gabbro*  .  .  . 
Sudbury  diabase    

Ohio  sandstone 

Plate  glass 


E 

0 

C 

2.H,  I(»0,fXK> 

0 

2HfX. 

1  1,<K)0,000 

I5.rKK),<KX> 

0 

2.500 

fi,00<t,IHK) 

I  i,070,fKXj 

n 

27SO 

4,.VV'.*'<'^o 

.S,{)46.0<K) 

0 

-•744 

3,154,1100 

7.S'.>-*,<x'<> 

0 

jfno 

3,o^x>.0(X> 

i),(K>6,<KH") 

0 

-'S>3 

3.f)07,ooo 

(J.JO'i.tXKl 

0 

2522 

3,636,tx)o 

6.8,^,1,0(X) 

0 

2528 

2,724,8<.X) 

S.JQS,™*' 

0 

2112 

3,399,000 

8,|65,0<X) 

0 

19H2 

3, 380,000 

7,,VU.."iOO 

0 

2 1 95 

3,019,700 

6,747,000 

0 

2152 

2,781,600 

8,247,, SCO 

0 

1077 

3,445,000 

5,685,000 

0 

25H5 

2,258,700 

9.137.,'ioo 

0 

2560 

3,635,000 

I  i,q6o,ooo 

0 

2620 

4,750,000 

9,746,000 

0 

25»3 

3,872,600 

I '5,650,000 

0 

2192 

6,365,000 

13,763,000 

0 

2840 

5,364,000 

2,290,000 

0 

2900 

888,000 

10,500,000 

0 

3273 

4,290,000 

I'm- 2' 


2*,  300, 000 

IO,0(K),0(X> 
8,303.000 

5,946,(K)0 
5,34i,fXKi 
5.967,<XK> 
6,167,500 

4,fj04,cxx) 
4,792,000 
4,517,500 

4..W7.,SOO 
3,984,000 
4,555,000 
3,940,000 

6,237,500 

8,368,000 
6,750,000 
9..'i.S5,ooo 
10,626,500 

1,816,000 

6,448,000 


Summary  op  Rbsolts  (Avbraoe)  Bxprbssbd  in  C.  O.  S.  Units. 


Wrought  iron iq  37  X  10" 

Cast  iron 10.34  X  '"" 

RIack  Belgian  marble.       .  7   24  X  m'' 

Carrara  marble 5  54  X  ii>" 

Vermont  marble 5   24  X  10" 

Tennessee  marble 6  21   X  10" 

Montreal  limestone '■  35  X  in" 

Haveno  granite 4.71   ,X  ni" 

Peterhead  granite    5  71   X  10" 

Lily  Lake  granite 5  63  X  10" 

Westerly  granite    5  09  X  i"" 

Quincy  granite  (1)     ...  4  64  >:  10" 

Quincy  granite  I  2) 5  6.s  x  10" 

Slanstead  granite 3  o.'  X  m" 

Nepheline  syenite fi.  jo  <  id" 

New  Glasgow  anortlKisitc  8   25  X  10" 

Mount  Johns<tn  essexite.  .  6.71  X  10" 

New  Glasgow  gabbrtj*.  .  .  10.80  X   10" 

Sudbury  diabase    9.49  X  if»" 

Ohio  sandstone 1 .  58  X  10" 

Plate  glass 7 .  24  X  10" 

*See  paiio  .S7 


0 

2800 

7.590  X  10" 

14  680  X 

10" 

0 

2.500 

4   >32 

X  1 

t 

6 .  897 

X 

10" 

0 

2780 

2.9S2 

X   1 

>" 

.S.7.1f> 

X 

10" 

0 

2744 

2     171 

X  1 

)" 

4  0(X1 

X 

1.1" 

0 

26  v> 

2    (tftt) 

X   1 

3 ,  680 

X 

10" 

0 

2513 

2    482 

X   I 

>" 

4    "S 

X 

to" 

0 

2522 

2    ,504 

X  1 

4   250 

X 

10" 

0 

2528 

■875 

X   1 

.1.  '7') 

X 

In" 

0 

21  12 

2    .U" 

X   I 

■V.V" 

X 

1.." 

0 

1982 

2    .3.10 

X   1 

3   '03 

X 

m" 

0 

2195 

2   080 

X    1 

3  "29 

X 

1,." 

0 

2I.S2 

1.916 

X    1 

) 

2 . 7.'iO 

X 

m" 

0 

1977 

2 .  37."- 

X   1 

l" 

3   >4" 

X 

in" 

0 

25f',S 

"  .S.56 

X  1 

2.71^ 

X 

in" 

0 

2560 

2    50.S 

X    1 

> 

4.  2I)0 

X 

10" 

0 

2620 

.1     275 

X   1 

1" 

S   760  X 

in" 

0 

2583 

2    670 

X   1 

4  f'.SO  X 

10" 

0 

2192 

4.3KO 

X  1 

)" 

6.589  X 

10" 

0 

2840 

3.700 

X  1 

7   329 

X 

in" 

0 

29fX) 

612 

X   I 

)" 

1 .  250  X 

10" 

0 

2273 

2.960  X  I 

>" 

4  439 

X 

10" 

MMk 


